{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-06T00:09:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-05-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":52774,"title":"Easy Sequences 23: Hat Guessing Game!","description":"Consider the following Game Show:\r\nHats, with numbers written on each, were placed on the heads of the participants. Participants can see the numbers on all hats, except their own. Each participant were asked to add all the numbers they do see and write the sum on a piece of paper card. The participants were then asked to hide their hats and show only their cards with numbers, to you, the contestant. For a prize of a million dollars, you were asked to guess the numbers written on each participant's hat.\r\nAssuming that all sums are correct, will you be the next millionare? Let's find out...","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 144px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eConsider the following Game Show:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eHats, with numbers written on each, were placed on the heads of the participants. Participants can see the numbers on all hats, except their own. Each participant were asked to add all the numbers they do see and write the sum on a piece of paper card. The participants were then asked to hide their hats and show only their cards with numbers, to you, the contestant. For a prize of a million dollars, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eyou were asked to guess the numbers written on each participant's hat.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eAssuming that all sums are correct, will you be the next millionare? Let's find out...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function nums = hatNumbers(sums)\r\n    nums = sums;\r\nend","test_suite":"%%\r\nsums = [667 658 645 688 629 625 713 630 637 678];\r\nnums_correct = [63 72 85 42 101 105 17 100 93 52];\r\nassert(isequal(hatNumbers(sums),nums_correct))\r\n%%\r\nsums = [1460 1459 1394 1416 1411 1428 1439 1394 1393 1395 1471 1470 ...\r\n        1469 1468 1395 1408 1407 1408 1395 1384 1439 1428 1406 1395 1460];\r\nnums_correct = [23 24 89 67 72 55 44 89 90 88 12 13 14 15 88 75 76 75 88 99 44 55 77 88 23];\r\nassert(isequal(hatNumbers(sums),nums_correct))\r\n%%\r\nsums = [ ...\r\n4892 4927 4901 4949 4896 4963 4939 4962 4957 4884 4897 4935 4871 4963 4923 4928 4890 4887 4948 4918 ...\r\n4922 4902 4896 4891 4939 4899 4901 4950 4955 4917 4871 4932 4908 4944 4891 4941 4916 4897 4877 4871 ...\r\n4912 4953 4952 4941 4882 4941 4885 4942 4874 4932 4947 4941 4905 4919 4931 4883 4908 4912 4875 4938 ...\r\n4891 4891 4928 4910 4959 4961 4913 4889 4873 4954 4910 4920 4965 4933 4950 4887 4935 4914 4950 4906 ...\r\n4940 4901 4898 4892 4921 4958 4944 4875 4951 4884 4913 4867 4959 4922 4956 4870 4966 4889 4885 4880 ...\r\n];\r\nnums = hatNumbers(sums);\r\nnums_stats = round([std(nums) mean(nums) mode(nums) median(nums)],4);\r\nassert(isequal(nums_stats,[28.8090 49.6700 26.0000 50.5000]))\r\n%%\r\nnums = randi(1000,1,1000).*97+2;\r\nsums = arrayfun(@(n) sum(nums(n-1:-1:1))+sum(nums(n+1:end)), 1:length(nums));\r\nassert(isequal(hatNumbers(sums),nums))\r\n%%\r\nfiletext = fileread('hatNumbers.m');\r\nblocked = {'solve' 'fsolve' 'dsolve' 'linsolve' 'mldivide' 'mrdivide' '\\' '/'};\r\nnot_allowed = any(arrayfun(@(s) contains(filetext, blocked{s}), 1:8));\r\nassert(~not_allowed)\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":"2021-09-24T08:03:12.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-22T11:19:54.000Z","updated_at":"2026-04-27T13:40:29.000Z","published_at":"2021-09-24T08:03:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the following Game Show:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHats, with numbers written on each, were placed on the heads of the participants. Participants can see the numbers on all hats, except their own. Each participant were asked to add all the numbers they do see and write the sum on a piece of paper card. The participants were then asked to hide their hats and show only their cards with numbers, to you, the contestant. For a prize of a million dollars, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eyou were asked to guess the numbers written on each participant's hat.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssuming that all sums are correct, will you be the next millionare? Let's find out...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52779,"title":"Easy Sequences 25: Product of Series","description":"The function 'P(n)' is defined as the series product:\r\n                            \r\nwhere 'T(n)' is the triangular sum:\r\n                            \r\nIt can be proven that P(n) is convergent, with:\r\n                            \r\nWrite a function that outputs the integer value of 'n' when '3 - P(n)' first becomes less than or equal to a given tolerance 't'.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 256px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe function 'P(n)' is defined as the series product:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"124.5\" height=\"46\" style=\"width: 124.5px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003ewhere 'T(n)' is the triangular sum:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"184\" height=\"19\" style=\"width: 184px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIt can be proven that P(n) is convergent, with:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 30px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"83.5\" height=\"29\" style=\"width: 83.5px; height: 29px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eWrite a function that outputs the integer value of 'n' when '3 - P(n)' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; text-decoration: underline; text-decoration-line: underline; \"\u003efirst\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e becomes less than or equal to a given tolerance 't'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = N(t)\r\n    n = N(t); \r\nend","test_suite":"%%\r\nt = 1;\r\nn_correct = 4;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.5;\r\nn_correct = 10;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.01;\r\nn_correct = 598;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.007;\r\nn_correct = 856;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.00032;\r\nn_correct = 18748;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nts = 10.^[-1:-1:-8]*3;\r\nns = arrayfun(@(t) N(t),ts); \r\nss_correct = 222222205;\r\nassert(isequal(sum(ns),ss_correct))\r\n%%\r\nt = 0.0000000026;\r\nn_correct = 2307692306;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nfiletext = fileread('n.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2021-09-24T21:04:32.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-24T20:12:14.000Z","updated_at":"2026-04-22T14:00:32.000Z","published_at":"2021-09-24T20:44:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function 'P(n)' is defined as the series product:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(n)=\\\\prod_{k=2}^{n}\\\\frac{T(k)}{T(k)-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere 'T(n)' is the triangular sum:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(n) = 1 + 2 + 3 + 4 + ...+n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt can be proven that P(n) is convergent, with:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lim_{n\\\\rightarrow \\\\infty}P(n) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that outputs the integer value of 'n' when '3 - P(n)' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efirst\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e becomes less than or equal to a given tolerance 't'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52824,"title":"Easy Sequences 31: N-N's Sequence","description":"We define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein any number  appears  times. The first few elements of this sequence are as follows:\r\n                        \r\nAs you can see,  appears  times,  appears  times,  appears  times, etc...\r\nWrite a function that output the number  occuping the  position.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 66px; transform-origin: 407px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376px 8px; transform-origin: 376px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein any number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.5px 8px; transform-origin: 192.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times. The first few elements of this sequence are as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48px 8px; transform-origin: 48px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 518px; height: 18.5px;\" width=\"518\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.5px 8px; transform-origin: 52.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs you can see, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5px 8px; transform-origin: 22.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e7\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e7\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5px 8px; transform-origin: 22.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38px 8px; transform-origin: 38px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times, etc...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140.5px 8px; transform-origin: 140.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWrite a function that output the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e occuping the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 26.5px; height: 18px;\" width=\"26.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.5px 8px; transform-origin: 32.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e position.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = nnPos(k)\r\n    n = k;\r\nend","test_suite":"%%\r\nk = 1;\r\nn_correct = 1;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = 20;\r\nn_correct = 6;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = 1000;\r\nn_correct = 45;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nks = 12345:12345:246900;\r\nns_correct = [157 222 272 314 351 385 416 444 471 497 521 544 567 588 609 629 648 667 685 703];\r\nassert(isequal(nnPos(ks),ns_correct))\r\n%%\r\nk = 2000000;\r\nn_correct = 2000;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = 123456789;\r\nn_correct = 15713;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = intmax;\r\nn_correct = 65536;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = intmax('int64');\r\nn_correct = 4294967296;\r\nassert(isequal(nnPos(k),n_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-28T18:15:10.000Z","updated_at":"2026-04-08T13:00:16.000Z","published_at":"2021-09-28T18:16:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein any number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times. The first few elements of this sequence are as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\left \\\\{ 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8 ...\\\\right \\\\} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs you can see, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times, etc...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that output the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e occuping the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\\\\mbox{-}th\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e position.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52654,"title":"Easy Sequences 13: Average Speed of Spaceship","description":"A certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ship travels from two points 's' km apart, at a speed of 'v' km/hr. After reaching its destination the spaceship immediately heads back to its starting point at the speed of 'v-1' km.hr. After reaching the starting point it again goes back at a speed of 'v-2'. This \"back and forth' continues, reducing the ship's speed by 1 km/hr in each turn around. \r\nGiven an integer initial velocity, find the average speed of the spaceship througout its entire journey, until it finally stops. Please round-off your answer to the nearest integer.\r\nNOTE: Use clasical physics only. Ignore any relativistic effects.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eA certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ship travels from two points 's' km apart, at a speed of 'v' km/hr. After reaching its destination the spaceship immediately heads back to its starting point at the speed of 'v-1' km.hr. After reaching the starting point it again goes back at a speed of 'v-2'. This \"back and forth' continues, reducing the ship's speed by 1 km/hr in each turn around.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven an integer initial velocity, find the average speed of the spaceship througout its entire journey, until it finally stops.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e Please round-off your answer to the nearest integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eNOTE: Use clasical physics only. Ignore any relativistic effects.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = mean_velocity(s,v)\r\n  y = x;\r\nend","test_suite":"%%\r\ns = 10000;\r\nv = 10000;\r\nv_correct = 1022;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = 1234567;\r\nv = 1234567;\r\nv_correct = 84539;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = '1234567891011121314151617181920';\r\nv = 123456789;\r\nv_correct = 6427156;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = 1e100;\r\nvs = 1:1000;\r\nv_correct = 72076;\r\nassert(isequal(sum(arrayfun(@(v) mean_velocity(s,v),vs)),v_correct))\r\n%%\r\ns = intmax;\r\nv = double(intmax);\r\nv_correct = 97326319;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = intmax('int64')/100;\r\nv = double(intmax('int64'))/100;\r\nv_correct = 2326765408587627;\r\nassert(isequal(mean_velocity(s,v),v_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2021-09-05T14:22:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-05T08:20:36.000Z","updated_at":"2026-04-08T12:51:29.000Z","published_at":"2021-09-05T08:20:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ship travels from two points 's' km apart, at a speed of 'v' km/hr. After reaching its destination the spaceship immediately heads back to its starting point at the speed of 'v-1' km.hr. After reaching the starting point it again goes back at a speed of 'v-2'. This \\\"back and forth' continues, reducing the ship's speed by 1 km/hr in each turn around.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an integer initial velocity, find the average speed of the spaceship througout its entire journey, until it finally stops.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Please round-off your answer to the nearest integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNOTE: Use clasical physics only. Ignore any relativistic effects.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52679,"title":"Easy Sequences 16: Volume of Embedded Octahedron","description":"An octahedron (not regular) is formed by joining the centers of the faces of a rectangular parallelepiped (see below figure).\r\n                                       \r\nGiven the dimensions of the rectangular parallelepiped (length, width and height), calculate the volume of the embedded octahedron. Please output the integer part of the volume in modulo 1000003.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 247px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eAn octahedron (not regular) is formed by joining the centers of the faces of a rectangular parallelepiped (see below figure).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 166px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                                       \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"311\" height=\"166\" style=\"vertical-align: middle;width: 311px;height: 166px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven the dimensions of the rectangular parallelepiped (length, width and height), calculate the volume of the embedded octahedron. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003ePlease output the integer part of the volume in modulo 1000003.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function v = volOcta(l,w,h)\r\n  y = x;\r\nend","test_suite":"%%\r\nl = 1234; w = 4567; h = 8910;\r\ny_correct = 956726;\r\nassert(isequal(volOcta(l,w,h),y_correct))\r\n%%\r\nl = 100000; w = 200000; h = 300000;\r\ny_correct = 9000;\r\nassert(isequal(volOcta(l,w,h),y_correct))\r\n%%\r\nls = 12:12:1440; ws = ls + 23; hs = ls .* 23;\r\ny_correct = 59634083;\r\nassert(isequal(sum(arrayfun(@(i) volOcta(ls(i),ws(i),hs(i)),1:length(ls))),y_correct))\r\n%%\r\nl = 12345678900; w = 353535353535; h = 12345678900;\r\ny_correct = 262344;\r\nassert(isequal(volOcta(l,w,h),y_correct))\r\n%%\r\nl = 14141414141414; w = 15151515151515; h = 16161616161616;\r\ny_correct = 541360;\r\nassert(isequal(volOcta(l,w,h),y_correct))\r\n%%\r\nfiletext = fileread('volOcta.m');\r\nnot_allowed = contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2021-09-11T14:45:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-09T20:56:03.000Z","updated_at":"2026-04-28T18:23:46.000Z","published_at":"2021-09-09T20:56:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn octahedron (not regular) is formed by joining the centers of the faces of a rectangular parallelepiped (see below figure).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                       \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"166\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"311\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the dimensions of the rectangular parallelepiped (length, width and height), calculate the volume of the embedded octahedron. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ePlease output the integer part of the volume in modulo 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Sequences 18: Set Bits of Triple Summations","description":"The function S(n) is defined by the following triple summations:\r\n                            \r\nThe double brackets mean that the output of the triple summations is being rounded-off to the nearest integer. Write the function 'bitS(n)', which is the number of bits set in the binary representation of S(n).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 127px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe function S(n) is defined by the following triple summations:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"186\" height=\"46\" style=\"width: 186px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe double brackets mean that the output of the triple summations is being rounded-off to the nearest integer. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eWrite the function 'bitS(n)', which is the number of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.quora.com/What-do-we-mean-by-a-set-bit\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ebits set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e in the binary representation of S(n).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = bitS(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 100;\r\ny_correct = 7;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 10000;\r\ny_correct = 17;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 1000000;\r\ny_correct = 19;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 100000000;\r\ny_correct = 25;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 12345678910;\r\ny_correct = 30;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nns = 1000:2000;\r\ny = sum(arrayfun(@(n) bitS(n),ns))\r\ny_correct = 10663;\r\nassert(isequal(y,y_correct))\r\n%%\r\nn = intmax-123;\r\ny_correct = 33;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = intmax('int64')-123456;\r\ny_correct = 74;\r\nassert(isequal(bitS(n),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-12T09:14:05.000Z","updated_at":"2025-12-22T16:36:34.000Z","published_at":"2021-09-12T10:34:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function S(n) is defined by the following triple summations:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(n)=\\\\left [\\\\sum_{k=2}^{n}\\\\sum_{j=2}^{k} \\\\sum_{i=2}^{j}\\\\frac{1}{\\\\log {_{i}}{\\\\left ( j! \\\\right )}}  \\\\right ]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe double brackets mean that the output of the triple summations is being rounded-off to the nearest integer. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite the function 'bitS(n)', which is the number of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.quora.com/What-do-we-mean-by-a-set-bit\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ebits set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e in the binary representation of S(n).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52809,"title":"Easy Sequences 28: Sum of Radicals of Integers","description":"The radical of a positive integer  is defined as the product of the distinct prime numbers dividing . For example, the distinct prime factors of  is , therefore the radical of  is . Similarly, the radicals of ,  and  are ,  and , respectively, The numberis considered to be the radical of itself.\r\nGiven a limit , find the sum of the radicals of all positive integers . \r\nFor , the radicals are: . Therefore, the output should be '41'.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 61.5px; transform-origin: 407px 61.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Radical_of_an_integer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eradical of a positive integer\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201px 8px; transform-origin: 201px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined as the product of the distinct prime numbers dividing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59px 8px; transform-origin: 59px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, the distinct prime factors of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAAkCAYAAAAkcgIJAAABYklEQVRYhe2XUbGDMBBFjwccxAAGqgAFOMBBHdQCGpCAh1pAAxb6PkgmGR4hu9n+NWeGjzJ7kr2Qpik0Go3GL+KArsJ5+Ktmvlr3dtAZ+AC90BmBDViAp/d3YKL8QCxulo4YIlySMMF5ne5P/v5605TFzTJwPJUBeCMPEybdMpOumWatrpgnsjAdx3K4m3DMjGVxVUjDTEndkKlxSU3atMVVIQ2TLkd3UxfewPYlV4U0TKjZC+Ot/G/c4qqQhOkrGxqMrhpJmEdlQ5PRVaMNsyjGO4fRumq0YdbCeC/yYbSump9bZlQ2FMazuCqkYTZlQztxe7W4KqRhZmFdqHl/yVUhDZOu/TFTk/6mpGve4qqQhoG4DHK7UtiNrk7GFleMJowjnp/OtenJ+Orfo8UV4Yhfzg9HsBK9n3hPmnLEw+TdMcTiZnEcr3W9uGbKa7bzNYt3Fv9ZsgNZ3Eaj0Wg0GiX+AJDSC8VPsu1pAAAAAElFTkSuQmCC\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 35.5px; height: 18.5px;\" width=\"35.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78px 8px; transform-origin: 78px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, therefore the radical of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAAkCAYAAAAkcgIJAAABYklEQVRYhe2XUbGDMBBFjwccxAAGqgAFOMBBHdQCGpCAh1pAAxb6PkgmGR4hu9n+NWeGjzJ7kr2Qpik0Go3GL+KArsJ5+Ktmvlr3dtAZ+AC90BmBDViAp/d3YKL8QCxulo4YIlySMMF5ne5P/v5605TFzTJwPJUBeCMPEybdMpOumWatrpgnsjAdx3K4m3DMjGVxVUjDTEndkKlxSU3atMVVIQ2TLkd3UxfewPYlV4U0TKjZC+Ot/G/c4qqQhOkrGxqMrhpJmEdlQ5PRVaMNsyjGO4fRumq0YdbCeC/yYbSump9bZlQ2FMazuCqkYTZlQztxe7W4KqRhZmFdqHl/yVUhDZOu/TFTk/6mpGve4qqQhoG4DHK7UtiNrk7GFleMJowjnp/OtenJ+Orfo8UV4Yhfzg9HsBK9n3hPmnLEw+TdMcTiZnEcr3W9uGbKa7bzNYt3Fv9ZsgNZ3Eaj0Wg0GiX+AJDSC8VPsu1pAAAAAElFTkSuQmCC\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Similarly, the radicals of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 18px;\" width=\"33\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e5\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABSklEQVRYhe2W4Y2DMAxG3w5swAIswARMwAZs0A26QmfICOzACsxwK/R+xFZdSkJCqHTS5ZOsthGJX4I/p1BVVfX31AC9fKaol+i+BbQAz4MEDfCQ52z8ANOVMDezeAiolcRbGBv3K2D6zaIhoBlYgdGMdXye2FAC0+B37Q6ABnkuBGtP2JUAOfzO7SntJXXEa6ThvZ5OacK/gjYB6CHPxTSXAHUysZffR0ApUqD5zOSFd0dcAbTK/Gz73wXINsBSoFbmagkkq2ffLaVA6rKs01GL700qAdJ1s2vHEe4RJUCOzxI41ITfxcDrUrQxGaDRjB8l0daR/ZrVkrkRSzSehQHvrDkSetM/5buOhxxTBJOinBoaEmA6Mu1/Fmjb4ffU4E/560AKs+D7TihWTl4fOUAKk2qGov9EmjBWyI64KWw4MntSVVVV1b/ULxZypElaY1O/AAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.5px 8px; transform-origin: 83.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, respectively, The number\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.5px 8px; transform-origin: 121.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis considered to be the radical of itself.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.5px 8px; transform-origin: 45.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182.5px 8px; transform-origin: 182.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the sum of the radicals of all positive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25px; height: 18px;\" width=\"25\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13px 8px; transform-origin: 13px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the radicals are: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 152.5px; height: 18.5px;\" width=\"152.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67px 8px; transform-origin: 67px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003ethe output should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11px 8px; transform-origin: 11px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003e'41'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = sumRadicals(n)\r\n    s = 41;\r\nend","test_suite":"%%\r\nn = 10;\r\ns_correct = 41;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 100;\r\ns_correct = 3512;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 1000;\r\ns_correct = 351964;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nns = 1000:5000;\r\nss = arrayfun(@(n) sumRadicals(n),ns);\r\nss_correct = [14572533416 1407530 2206262 3168720 4321316 5635156 7128944 8813000 2478567];\r\nassert(isequal([sum(ss) ss(1000:500:4000) floor(std(ss))],ss_correct))\r\n%%\r\nn = 10000;\r\ns_correct = 35252550;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 100000;\r\ns_correct = 3522204030;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 1000000;\r\ns_correct = 352218412502;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nfiletext = fileread('sumRadicals.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-27T09:04:12.000Z","updated_at":"2026-04-08T13:04:36.000Z","published_at":"2021-09-27T10:53:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Radical_of_an_integer\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eradical of a positive integer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as the product of the distinct prime numbers dividing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For example, the distinct prime factors of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[2\\\\ 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, therefore the radical of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Similarly, the radicals of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e125\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1344\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, respectively, The number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis considered to be the radical of itself.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the sum of the radicals of all positive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\leq n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the radicals are: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1, 2, 3, 2, 5, 6, 7, 2, 3, 10]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe output should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'41'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52814,"title":"Easy Sequences 27: Product of Radicals of Integers","description":"The radical of a positive integer  is defined as the product of the distinct prime numbers dividing . For example, the distinct prime factors of  is , therefore the radical of  is . Similarly, the radicals of ,  and  are ,  and , respectively, The numberis considered to be the radical of itself.\r\nGiven a limit , find the product of the radicals of all positive integers . Since, the radical product can get huge fast, please output only the number of digits of the product.\r\nFor , the radicals are: , their product is . Therefore, the output should be '6' digits","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 144px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 72px; transform-origin: 407px 72px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Radical_of_an_integer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eradical of a positive integer\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201px 8px; transform-origin: 201px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined as the product of the distinct prime numbers dividing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59px 8px; transform-origin: 59px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, the distinct prime factors of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 35.5px; height: 18.5px;\" width=\"35.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78px 8px; transform-origin: 78px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, therefore the radical of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAAkCAYAAAAkcgIJAAABYklEQVRYhe2XUbGDMBBFjwccxAAGqgAFOMBBHdQCGpCAh1pAAxb6PkgmGR4hu9n+NWeGjzJ7kr2Qpik0Go3GL+KArsJ5+Ktmvlr3dtAZ+AC90BmBDViAp/d3YKL8QCxulo4YIlySMMF5ne5P/v5605TFzTJwPJUBeCMPEybdMpOumWatrpgnsjAdx3K4m3DMjGVxVUjDTEndkKlxSU3atMVVIQ2TLkd3UxfewPYlV4U0TKjZC+Ot/G/c4qqQhOkrGxqMrhpJmEdlQ5PRVaMNsyjGO4fRumq0YdbCeC/yYbSump9bZlQ2FMazuCqkYTZlQztxe7W4KqRhZmFdqHl/yVUhDZOu/TFTk/6mpGve4qqQhoG4DHK7UtiNrk7GFleMJowjnp/OtenJ+Orfo8UV4Yhfzg9HsBK9n3hPmnLEw+TdMcTiZnEcr3W9uGbKa7bzNYt3Fv9ZsgNZ3Eaj0Wg0GiX+AJDSC8VPsu1pAAAAAElFTkSuQmCC\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Similarly, the radicals of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 18px;\" width=\"33\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e5\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.5px 8px; transform-origin: 83.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, respectively, The number\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.5px 8px; transform-origin: 121.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis considered to be the radical of itself.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.5px 8px; transform-origin: 45.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.5px 8px; transform-origin: 195.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the product of the radicals of all positive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25px; height: 18px;\" width=\"25\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 110px 8px; transform-origin: 110px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Since, the radical product can get huge fast, please output only the number of digits of the product.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13px 8px; transform-origin: 13px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the radicals are: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 152.5px; height: 18.5px;\" width=\"152.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53px 8px; transform-origin: 53px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, their product is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG0AAAAkCAYAAACDr7TyAAAC+UlEQVRoge2aXbWsMAyFtwccYAADKEABDo4DHGBhNIyE8TAW0ICFuQ9tFqG3LQmlzFn35lurL3OaJuzQ9IcDGIZhGIZhGEYtWgCNon8HoE+0hx+vht8ztNhiO+OLbKXPdJVtkhZO5A9cIiQ0AFZvE2uvSn61DACWRHxHIlJ8K4DJt8XbHsVbYpulwSYaNemAE9IJ+8C9WTX8apgPYlyRTlzn/74EsTXYXoKhgm2WAU74AcAbOvFolv3c7FdD78flZboBMGI/894RWy5u7Blp7A/+LrUltir4rJGI94P8W1rLr4Y3XMJihKU99E1x5Z6REvO80FaFVrwFTpSzi/pZv1I6uBhzsfHSGc4ISmhsFhK8vHM/JbYqNOKNrC8vMeOJAGolbcBx6eZlivcd2O+pmQpvQ/3GC2zVaMSL7cT4wp7bgJT4vRqeNB4zjymXeG5PCSqxVaMVr4d7q2bEkyjdGX0zaVQxwjL6hF54KoUltmpKxRuxX9hXyErlN5NG68oU/P6CXvj1Als1V4jXYL+FD8Wo5fcMtHuMbVa48Ecx5ZKmtVVzlXgtthknuRH5VtLIb2z95cIfXRDkkqa1VXOleFR2JMF8I2kd8ru2/6o8ErTt/Y1Jo9uKWRiTVHg6JJfYqrlSPApoudnvEbTm5hIG7M+hUuFpzBJbNTVmmuT8cVfSpAkD3LosmQU8djrilNiqqbGmSYK5K2mShPF4aW3KVYsn68N3oCW2KqTiNch/zKM3TbJz1PiF9ztBf132EMQzYl8ZUrclBN/9hWWwxFaFVDx+gJ6wF49K0PtgjDN+ednRLN4062dsHyLDRn1CgelCOeaL4k69DCW2Ilrsr6Jyh2K+paXpPfkgVzgBpLNA47fD3u8Hx5+Fwo+suZa6SuJJp+eiy94X8s9aYpuk9QO+Iu2B9NQd4d4g3neC7v9BzvidfB+6dcn5GxLjp1rupr0P4p0h3zyU2P5T9JAdJ4xfxBOFC7hxLw8UHEaN+xlR8JXXMAzDMAzDEPAHvaP26LcvqHsAAAAASUVORK5CYII=\" style=\"width: 54.5px; height: 18px;\" width=\"54.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.5px 8px; transform-origin: 68.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003ethe output should be '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.5px 8px; transform-origin: 5.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003e6'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.5px 8px; transform-origin: 18.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e digits\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = prodRadicals(n)\r\n    r = 6;\r\nend","test_suite":"%%\r\nn = 10;\r\nr_correct = 6;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nn = 1000;\r\nr_correct = 2263;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nns = 10000:50000;\r\nrs = arrayfun(@(n) prodRadicals(n),ns);\r\nss_correct = [4503407257 70876 91001 111568 132490 153727 175243 196990 47696];\r\nassert(isequal([sum(rs) rs(10000:5000:40000) floor(std(rs))],ss_correct))\r\n%%\r\nn = 1000000;\r\nr_correct = 5238328;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nn = 1000000000;\r\nr_correct = 8237674403;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nn = intmax;\r\nr_correct = 18403071064;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nfiletext = fileread('prodRadicals.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-27T09:04:14.000Z","updated_at":"2026-04-22T13:56:23.000Z","published_at":"2021-09-27T10:28:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Radical_of_an_integer\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eradical of a positive integer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as the product of the distinct prime numbers dividing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For example, the distinct prime factors of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[2\\\\ 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, therefore the radical of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Similarly, the radicals of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e125\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1344\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, respectively, The number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis considered to be the radical of itself.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the product of the radicals of all positive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\leq n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Since, the radical product can get huge fast, please output only the number of digits of the product.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the radicals are: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1, 2, 3, 2, 5, 6, 7, 2, 3, 10]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, their product is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e151,200\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe output should be '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e6'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e digits\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":52774,"title":"Easy Sequences 23: Hat Guessing Game!","description":"Consider the following Game Show:\r\nHats, with numbers written on each, were placed on the heads of the participants. Participants can see the numbers on all hats, except their own. Each participant were asked to add all the numbers they do see and write the sum on a piece of paper card. The participants were then asked to hide their hats and show only their cards with numbers, to you, the contestant. For a prize of a million dollars, you were asked to guess the numbers written on each participant's hat.\r\nAssuming that all sums are correct, will you be the next millionare? Let's find out...","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 144px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eConsider the following Game Show:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eHats, with numbers written on each, were placed on the heads of the participants. Participants can see the numbers on all hats, except their own. Each participant were asked to add all the numbers they do see and write the sum on a piece of paper card. The participants were then asked to hide their hats and show only their cards with numbers, to you, the contestant. For a prize of a million dollars, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eyou were asked to guess the numbers written on each participant's hat.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eAssuming that all sums are correct, will you be the next millionare? Let's find out...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function nums = hatNumbers(sums)\r\n    nums = sums;\r\nend","test_suite":"%%\r\nsums = [667 658 645 688 629 625 713 630 637 678];\r\nnums_correct = [63 72 85 42 101 105 17 100 93 52];\r\nassert(isequal(hatNumbers(sums),nums_correct))\r\n%%\r\nsums = [1460 1459 1394 1416 1411 1428 1439 1394 1393 1395 1471 1470 ...\r\n        1469 1468 1395 1408 1407 1408 1395 1384 1439 1428 1406 1395 1460];\r\nnums_correct = [23 24 89 67 72 55 44 89 90 88 12 13 14 15 88 75 76 75 88 99 44 55 77 88 23];\r\nassert(isequal(hatNumbers(sums),nums_correct))\r\n%%\r\nsums = [ ...\r\n4892 4927 4901 4949 4896 4963 4939 4962 4957 4884 4897 4935 4871 4963 4923 4928 4890 4887 4948 4918 ...\r\n4922 4902 4896 4891 4939 4899 4901 4950 4955 4917 4871 4932 4908 4944 4891 4941 4916 4897 4877 4871 ...\r\n4912 4953 4952 4941 4882 4941 4885 4942 4874 4932 4947 4941 4905 4919 4931 4883 4908 4912 4875 4938 ...\r\n4891 4891 4928 4910 4959 4961 4913 4889 4873 4954 4910 4920 4965 4933 4950 4887 4935 4914 4950 4906 ...\r\n4940 4901 4898 4892 4921 4958 4944 4875 4951 4884 4913 4867 4959 4922 4956 4870 4966 4889 4885 4880 ...\r\n];\r\nnums = hatNumbers(sums);\r\nnums_stats = round([std(nums) mean(nums) mode(nums) median(nums)],4);\r\nassert(isequal(nums_stats,[28.8090 49.6700 26.0000 50.5000]))\r\n%%\r\nnums = randi(1000,1,1000).*97+2;\r\nsums = arrayfun(@(n) sum(nums(n-1:-1:1))+sum(nums(n+1:end)), 1:length(nums));\r\nassert(isequal(hatNumbers(sums),nums))\r\n%%\r\nfiletext = fileread('hatNumbers.m');\r\nblocked = {'solve' 'fsolve' 'dsolve' 'linsolve' 'mldivide' 'mrdivide' '\\' '/'};\r\nnot_allowed = any(arrayfun(@(s) contains(filetext, blocked{s}), 1:8));\r\nassert(~not_allowed)\r\n\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":30,"test_suite_updated_at":"2021-09-24T08:03:12.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-22T11:19:54.000Z","updated_at":"2026-04-27T13:40:29.000Z","published_at":"2021-09-24T08:03:12.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eConsider the following Game Show:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eHats, with numbers written on each, were placed on the heads of the participants. Participants can see the numbers on all hats, except their own. Each participant were asked to add all the numbers they do see and write the sum on a piece of paper card. The participants were then asked to hide their hats and show only their cards with numbers, to you, the contestant. For a prize of a million dollars, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eyou were asked to guess the numbers written on each participant's hat.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAssuming that all sums are correct, will you be the next millionare? Let's find out...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52779,"title":"Easy Sequences 25: Product of Series","description":"The function 'P(n)' is defined as the series product:\r\n                            \r\nwhere 'T(n)' is the triangular sum:\r\n                            \r\nIt can be proven that P(n) is convergent, with:\r\n                            \r\nWrite a function that outputs the integer value of 'n' when '3 - P(n)' first becomes less than or equal to a given tolerance 't'.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 256px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe function 'P(n)' is defined as the series product:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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VkUvz15ikfQ3Gc8yuU599HlYhk5j46DPCGmRGD88Gzff76cR5yZbp1QcKB5tr0mpS2PtG+Rp86U0gRzeOaFtp6zm9ijjwrh55kJOnrcKmFJPu8cC/PDroax2WfwifbCS5tFdqhwpMDHFxEo8JmLMivKWReYIYYkxovT4kEd/ERodCd0X5YtkZwahCUWEXcYt4BZYY4EhSlhhDAeVMAwhNKE3IX7aKp+m6n4x6evVULmp0j1TwLYljRaLSftd0ioryiu9klf0OXxYHWqBczVuc/A/K8/+uygRGdB2TsEGODTnE7SZEdpsq5QbBPb8No6XlD9GSKPrxURuYlplRXmlndzD9Yq+yQ4dVhyqEz7jbEVpQBBkr1+EDpBQnyB4b0i5ez9DeEdgkrHDxBuUT6PnAnOntMr1hbfR+vIg/hxttwDh9oHRKH4e5Ytk+wehtL16WvvkhIIMOjgHeEXgS7jnhTyyvqzvPNmOrfOVvGNfXeUGjoPj6EZph25Wl5buGJivp1Wm8OzQjdV4kcB5ADcNLwv7C7UcXCJ/P/xbr53cV3JetVMzLBCvrPOkcH5JpTsE+TcKtGPvjVND9wrHCFcJ1wnc3a8UihAHfdBWa5LCf++Q5PDC0umC48UuG+2ka6rBdSevYaA2Ve+rfv9V4D/v+gkjhGbRblI0UUA3K+CDAs7BAVQjNDZqPCvKF83yYQoURwNrOOv+PUQsruKgw4XThVXC2UJRB5fo3/+jsUwb2m0ufIRMA9S7gbalmrqTlzJXtwkvVk9vC3zddGsTez006Nsk0snh1CjhZIHrq3poezX6ZNSwnhVqQWhf5PpsdNTXwJDfUOkJwhVRXa2s9WV915K3+mnK7GyFOtMn62znzdYjCxCCsrp+uUnPhGPzY/6uwGq+t3CJQB8gPjRTsRQRepqed5Xneqss8cUaOqYXaDg/yHYp3UNgQqTts4Kt8MrWpMmSoN3FNSWrI+BXaNV5Fw2P5OCggT1nM4gQ92HhXIFDKe6jzxR+KkCs5vXSmKjhbOVxurJkqynbkzzaVZUDg8BNSp8Sbgzlf1L6qZAvktg5gPVdpE3HyfjpenVf2WgNbaEwr0lDxPG+kaLr0cB7K6WuKCt28geKNkrIPRfKw5Xm/S6xi5FNgJcaQymrsxGyTG5ZdFComJslUEF+mUilgsP3IZkF2O8RRs4IjOuU4oy/FS4IvGYlhMf0tWedCnEU2htiJyyrkudDz9CchjcHGbYF8dnCPYFP+yMFTsxfEQhv02gbMTmDYCLNm1TS2raTN0Gdm62JZJw61AITNW5e5PFh/Kcq5TDOVqVrlGflLYqjJZtF7GM5BKpnhdhH7Yg07EdHep7QW6iHbF+OjjTicG2pQD/3JwT2UxmnpW6ZwJaECSGLPqcKZDmj6BT6Rw2UqINxg9eEwYJTB1qAfTIvkf0pP/yHBU6wjU5U5soSGGYNE+kolZko2MuWIeS5z7YfWzJ9W3U/EsoSqy8rNA6KQyfp42JYX19LVqp8YVSPM2yZImMsQn10xbcCVle1dEcN6FXBJjGzASm8LuEUwalDLEDoyFdfLwjfFwhDNxWaTTjU74Xjmq24QX2XqT0/3gl16mEiGCP0yWl/sOro48YcGa9yC7TMAlxt8QM0zGxBTxtLJ+Hu1BboblQlzsn5w4sC42wFzZZSJtHNW6HcdboFalmA/SgOzj78EYFwbFchpmtUKLofR+7TUWPC4P8VWDGT1DfJaFN5kPpdIvy4Bf1zw7BcGNoC3ZVUuVElR9WzB8XpNI5NKMnelgOls4XThCHCSwIr0QqhKC0Oghyu/VBA7xmBZ8kkZbYTphmjjel89c2h450CzztFaAaNlxKil68IjzdDoetwC5S1ACvpOwLhKtRb6BJw6H8THhAa2Z9fqvZ/E34lPBjhGeVXCgOEKtEEDYZVl5PwRmmEFHCo16wJo9HxePseaoGD9Nw44YXR849THgdcJoyK+GWzp6gBurMws6zCbpL/Z/WzVxP6Giwdw5ugx1W4BVpigf7SullLNLtSt4BbwC3gFnALuAXcAm4Bt4BbwC3gFnALuAXcAm4Bt4BbwC3gFnALuAXcAm6BhAX+Hz1CdtCCThCbAAAAAElFTkSuQmCC\" width=\"124.5\" height=\"46\" style=\"width: 124.5px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003ewhere 'T(n)' is the triangular sum:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"184\" height=\"19\" style=\"width: 184px; height: 19px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eIt can be proven that P(n) is convergent, with:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 30px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-15px\"\u003e\u003cimg src=\"data:image/png;base64,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\" width=\"83.5\" height=\"29\" style=\"width: 83.5px; height: 29px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eWrite a function that outputs the integer value of 'n' when '3 - P(n)' \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; text-decoration: underline; text-decoration-line: underline; \"\u003efirst\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e becomes less than or equal to a given tolerance 't'.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = N(t)\r\n    n = N(t); \r\nend","test_suite":"%%\r\nt = 1;\r\nn_correct = 4;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.5;\r\nn_correct = 10;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.01;\r\nn_correct = 598;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.007;\r\nn_correct = 856;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nt = 0.00032;\r\nn_correct = 18748;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nts = 10.^[-1:-1:-8]*3;\r\nns = arrayfun(@(t) N(t),ts); \r\nss_correct = 222222205;\r\nassert(isequal(sum(ns),ss_correct))\r\n%%\r\nt = 0.0000000026;\r\nn_correct = 2307692306;\r\nassert(isequal(N(t),n_correct))\r\n%%\r\nfiletext = fileread('n.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)\r\n","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2021-09-24T21:04:32.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-24T20:12:14.000Z","updated_at":"2026-04-22T14:00:32.000Z","published_at":"2021-09-24T20:44:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function 'P(n)' is defined as the series product:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eP(n)=\\\\prod_{k=2}^{n}\\\\frac{T(k)}{T(k)-1}\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ewhere 'T(n)' is the triangular sum:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eT(n) = 1 + 2 + 3 + 4 + ...+n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIt can be proven that P(n) is convergent, with:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\lim_{n\\\\rightarrow \\\\infty}P(n) = 3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that outputs the integer value of 'n' when '3 - P(n)' \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003efirst\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e becomes less than or equal to a given tolerance 't'.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52824,"title":"Easy Sequences 31: N-N's Sequence","description":"We define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein any number  appears  times. The first few elements of this sequence are as follows:\r\n                        \r\nAs you can see,  appears  times,  appears  times,  appears  times, etc...\r\nWrite a function that output the number  occuping the  position.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 132px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 66px; transform-origin: 407px 66px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 376px 8px; transform-origin: 376px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eWe define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein any number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 192.5px 8px; transform-origin: 192.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times. The first few elements of this sequence are as follows:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 48px 8px; transform-origin: 48px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e                        \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 518px; height: 18.5px;\" width=\"518\" height=\"18.5\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.5px 8px; transform-origin: 52.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eAs you can see, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e4\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5px 8px; transform-origin: 22.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e7\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e7\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 22.5px 8px; transform-origin: 22.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 30px 8px; transform-origin: 30px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e appears \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 38px 8px; transform-origin: 38px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e times, etc...\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 140.5px 8px; transform-origin: 140.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eWrite a function that output the number \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 50px 8px; transform-origin: 50px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e occuping the \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 26.5px; height: 18px;\" width=\"26.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 32.5px 8px; transform-origin: 32.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e position.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function n = nnPos(k)\r\n    n = k;\r\nend","test_suite":"%%\r\nk = 1;\r\nn_correct = 1;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = 20;\r\nn_correct = 6;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = 1000;\r\nn_correct = 45;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nks = 12345:12345:246900;\r\nns_correct = [157 222 272 314 351 385 416 444 471 497 521 544 567 588 609 629 648 667 685 703];\r\nassert(isequal(nnPos(ks),ns_correct))\r\n%%\r\nk = 2000000;\r\nn_correct = 2000;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = 123456789;\r\nn_correct = 15713;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = intmax;\r\nn_correct = 65536;\r\nassert(isequal(nnPos(k),n_correct))\r\n%%\r\nk = intmax('int64');\r\nn_correct = 4294967296;\r\nassert(isequal(nnPos(k),n_correct))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":15,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-28T18:15:10.000Z","updated_at":"2026-04-08T13:00:16.000Z","published_at":"2021-09-28T18:16:17.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWe define the N-N's Sequence, as the series of all positive integers in ascending order and with repetition, wherein any number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times. The first few elements of this sequence are as follows:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                        \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\left \\\\{ 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8 ...\\\\right \\\\} \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAs you can see, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e4\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e7\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e appears \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e times, etc...\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite a function that output the number \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e occuping the \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ek\\\\mbox{-}th\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e position.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52654,"title":"Easy Sequences 13: Average Speed of Spaceship","description":"A certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ship travels from two points 's' km apart, at a speed of 'v' km/hr. After reaching its destination the spaceship immediately heads back to its starting point at the speed of 'v-1' km.hr. After reaching the starting point it again goes back at a speed of 'v-2'. This \"back and forth' continues, reducing the ship's speed by 1 km/hr in each turn around. \r\nGiven an integer initial velocity, find the average speed of the spaceship througout its entire journey, until it finally stops. Please round-off your answer to the nearest integer.\r\nNOTE: Use clasical physics only. Ignore any relativistic effects.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 165px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eA certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ship travels from two points 's' km apart, at a speed of 'v' km/hr. After reaching its destination the spaceship immediately heads back to its starting point at the speed of 'v-1' km.hr. After reaching the starting point it again goes back at a speed of 'v-2'. This \"back and forth' continues, reducing the ship's speed by 1 km/hr in each turn around.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven an integer initial velocity, find the average speed of the spaceship througout its entire journey, until it finally stops.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e Please round-off your answer to the nearest integer.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eNOTE: Use clasical physics only. Ignore any relativistic effects.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = mean_velocity(s,v)\r\n  y = x;\r\nend","test_suite":"%%\r\ns = 10000;\r\nv = 10000;\r\nv_correct = 1022;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = 1234567;\r\nv = 1234567;\r\nv_correct = 84539;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = '1234567891011121314151617181920';\r\nv = 123456789;\r\nv_correct = 6427156;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = 1e100;\r\nvs = 1:1000;\r\nv_correct = 72076;\r\nassert(isequal(sum(arrayfun(@(v) mean_velocity(s,v),vs)),v_correct))\r\n%%\r\ns = intmax;\r\nv = double(intmax);\r\nv_correct = 97326319;\r\nassert(isequal(mean_velocity(s,v),v_correct))\r\n%%\r\ns = intmax('int64')/100;\r\nv = double(intmax('int64'))/100;\r\nv_correct = 2326765408587627;\r\nassert(isequal(mean_velocity(s,v),v_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":4,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":18,"test_suite_updated_at":"2021-09-05T14:22:29.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-05T08:20:36.000Z","updated_at":"2026-04-08T12:51:29.000Z","published_at":"2021-09-05T08:20:36.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eA certain alien spaceship is capable of traveling at extremely high velocities and is able to change speed instantaneously. The ship travels from two points 's' km apart, at a speed of 'v' km/hr. After reaching its destination the spaceship immediately heads back to its starting point at the speed of 'v-1' km.hr. After reaching the starting point it again goes back at a speed of 'v-2'. This \\\"back and forth' continues, reducing the ship's speed by 1 km/hr in each turn around.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven an integer initial velocity, find the average speed of the spaceship througout its entire journey, until it finally stops.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Please round-off your answer to the nearest integer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eNOTE: Use clasical physics only. Ignore any relativistic effects.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52679,"title":"Easy Sequences 16: Volume of Embedded Octahedron","description":"An octahedron (not regular) is formed by joining the centers of the faces of a rectangular parallelepiped (see below figure).\r\n                                       \r\nGiven the dimensions of the rectangular parallelepiped (length, width and height), calculate the volume of the embedded octahedron. Please output the integer part of the volume in modulo 1000003.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 247px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eAn octahedron (not regular) is formed by joining the centers of the faces of a rectangular parallelepiped (see below figure).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 166px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                                       \u003c/span\u003e\u003c/span\u003e\u003cimg class=\"imageNode\" width=\"311\" height=\"166\" style=\"vertical-align: middle;width: 311px;height: 166px\" 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\" data-image-state=\"image-loaded\"\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eGiven the dimensions of the rectangular parallelepiped (length, width and height), calculate the volume of the embedded octahedron. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003ePlease output the integer part of the volume in modulo 1000003.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function v = volOcta(l,w,h)\r\n  y = x;\r\nend","test_suite":"%%\r\nl = 1234; w = 4567; h = 8910;\r\ny_correct = 956726;\r\nassert(isequal(volOcta(l,w,h),y_correct))\r\n%%\r\nl = 100000; w = 200000; h = 300000;\r\ny_correct = 9000;\r\nassert(isequal(volOcta(l,w,h),y_correct))\r\n%%\r\nls = 12:12:1440; ws = ls + 23; hs = ls .* 23;\r\ny_correct = 59634083;\r\nassert(isequal(sum(arrayfun(@(i) volOcta(ls(i),ws(i),hs(i)),1:length(ls))),y_correct))\r\n%%\r\nl = 12345678900; w = 353535353535; h = 12345678900;\r\ny_correct = 262344;\r\nassert(isequal(volOcta(l,w,h),y_correct))\r\n%%\r\nl = 14141414141414; w = 15151515151515; h = 16161616161616;\r\ny_correct = 541360;\r\nassert(isequal(volOcta(l,w,h),y_correct))\r\n%%\r\nfiletext = fileread('volOcta.m');\r\nnot_allowed = contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)\r\n","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":"2021-09-11T14:45:58.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-09T20:56:03.000Z","updated_at":"2026-04-28T18:23:46.000Z","published_at":"2021-09-09T20:56:03.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAn octahedron (not regular) is formed by joining the centers of the faces of a rectangular parallelepiped (see below figure).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                                       \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"image\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"height\\\" w:val=\\\"166\\\"/\u003e\u003cw:attr w:name=\\\"width\\\" w:val=\\\"311\\\"/\u003e\u003cw:attr w:name=\\\"verticalAlign\\\" w:val=\\\"middle\\\"/\u003e\u003cw:attr w:name=\\\"altText\\\" w:val=\\\"\\\"/\u003e\u003cw:attr w:name=\\\"relationshipId\\\" w:val=\\\"rId1\\\"/\u003e\u003c/w:customXmlPr\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven the dimensions of the rectangular parallelepiped (length, width and height), calculate the volume of the embedded octahedron. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003ePlease output the integer part of the volume in modulo 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Sequences 18: Set Bits of Triple Summations","description":"The function S(n) is defined by the following triple summations:\r\n                            \r\nThe double brackets mean that the output of the triple summations is being rounded-off to the nearest integer. Write the function 'bitS(n)', which is the number of bits set in the binary representation of S(n).","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; \"\u003e\u003cdiv style=\"block-size: 127px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe function S(n) is defined by the following triple summations:\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003e                            \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-17px\"\u003e\u003cimg 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\" width=\"186\" height=\"46\" style=\"width: 186px; height: 46px;\"\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"\"\u003eThe double brackets mean that the output of the triple summations is being rounded-off to the nearest integer. \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003eWrite the function 'bitS(n)', which is the number of \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://www.quora.com/What-do-we-mean-by-a-set-bit\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003ebits set\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; \"\u003e\u003cspan style=\"font-weight: bold; \"\u003e in the binary representation of S(n).\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function y = bitS(n)\r\n  y = x;\r\nend","test_suite":"%%\r\nn = 100;\r\ny_correct = 7;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 10000;\r\ny_correct = 17;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 1000000;\r\ny_correct = 19;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 100000000;\r\ny_correct = 25;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = 12345678910;\r\ny_correct = 30;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nns = 1000:2000;\r\ny = sum(arrayfun(@(n) bitS(n),ns))\r\ny_correct = 10663;\r\nassert(isequal(y,y_correct))\r\n%%\r\nn = intmax-123;\r\ny_correct = 33;\r\nassert(isequal(bitS(n),y_correct))\r\n%%\r\nn = intmax('int64')-123456;\r\ny_correct = 74;\r\nassert(isequal(bitS(n),y_correct))","published":true,"deleted":false,"likes_count":2,"comments_count":5,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":8,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-12T09:14:05.000Z","updated_at":"2025-12-22T16:36:34.000Z","published_at":"2021-09-12T10:34:16.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe function S(n) is defined by the following triple summations:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e                            \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003eS(n)=\\\\left [\\\\sum_{k=2}^{n}\\\\sum_{j=2}^{k} \\\\sum_{i=2}^{j}\\\\frac{1}{\\\\log {_{i}}{\\\\left ( j! \\\\right )}}  \\\\right ]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe double brackets mean that the output of the triple summations is being rounded-off to the nearest integer. \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eWrite the function 'bitS(n)', which is the number of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://www.quora.com/What-do-we-mean-by-a-set-bit\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ebits set\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e in the binary representation of S(n).\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52809,"title":"Easy Sequences 28: Sum of Radicals of Integers","description":"The radical of a positive integer  is defined as the product of the distinct prime numbers dividing . For example, the distinct prime factors of  is , therefore the radical of  is . Similarly, the radicals of ,  and  are ,  and , respectively, The numberis considered to be the radical of itself.\r\nGiven a limit , find the sum of the radicals of all positive integers . \r\nFor , the radicals are: . Therefore, the output should be '41'.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 123px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 61.5px; transform-origin: 407px 61.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Radical_of_an_integer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eradical of a positive integer\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201px 8px; transform-origin: 201px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined as the product of the distinct prime numbers dividing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59px 8px; transform-origin: 59px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, the distinct prime factors of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 35.5px; height: 18.5px;\" width=\"35.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78px 8px; transform-origin: 78px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, therefore the radical of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Similarly, the radicals of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 33px; height: 18px;\" width=\"33\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e5\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.5px 8px; transform-origin: 83.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, respectively, The number\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.5px 8px; transform-origin: 121.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis considered to be the radical of itself.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.5px 8px; transform-origin: 45.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 182.5px 8px; transform-origin: 182.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the sum of the radicals of all positive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25px; height: 18px;\" width=\"25\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13px 8px; transform-origin: 13px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFgAAAAkCAYAAAANdf2OAAACA0lEQVRoge2YXZWDMBBGr4c4wAAGqqAKcFAHOKiFakACHrBQDVjYfWjmMLDZMCndU+jOPScvZPLDl8lkEnAcx3Ecx3HKCUD1RJtTLOHlM/oQAtACI3AxtjkBPTDEttfY/kr5In00IuxXLBaBm2jbM/faOn4fcZGpeHhbA9ywC1wr2zpR38a64WUz/QBO2AXuyQtYFfT1b7AKrL33mrG74148wyrwVdk1GbtO2RXH4sDP2FPFSR41sFsF7snHX6HFthAAnGODnum0lUlUi0HHlYGX6BxyS9m6sFaBdbZhFTgXSoDJOyWuiNvXccC2tEOF/rEtZethYhVYj2kVuLNOYmDK/Srm3qonuLolFHXsb2s5F4yZolTgsaA/k8BhMYGBuZAXVX/E6+IzAuf+80yhwLpBzyMx19xU3RF5e4jQN517ol6Cf2vpbIf8ZRZhOh/0AbeMd2tXxxxHyyK0o1kFXj0ftIApd5f4uxb4Uxwti2iMduLppkcffYClVkM6W8ZlC0fLIgJTOMz9r9iY4q9ejdSAy/SsozxUvJuSxx7Z/r9lEjohMOkgxqkV01smRJuSi8ZeKBEYpjtBylYc0nTg69VIbUMdPgYKbi07IjB/nOlYz+UDk8iN+iaHoNnJGqY4l5tcT9kNbi/IG8uydLFuTWh5rJd2LccLj47jOI7jOI7jHJ1vW/g1szUietQAAAAASUVORK5CYII=\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the radicals are: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 152.5px; height: 18.5px;\" width=\"152.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 67px 8px; transform-origin: 67px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003ethe output should be \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11px 8px; transform-origin: 11px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003e'41'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function s = sumRadicals(n)\r\n    s = 41;\r\nend","test_suite":"%%\r\nn = 10;\r\ns_correct = 41;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 100;\r\ns_correct = 3512;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 1000;\r\ns_correct = 351964;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nns = 1000:5000;\r\nss = arrayfun(@(n) sumRadicals(n),ns);\r\nss_correct = [14572533416 1407530 2206262 3168720 4321316 5635156 7128944 8813000 2478567];\r\nassert(isequal([sum(ss) ss(1000:500:4000) floor(std(ss))],ss_correct))\r\n%%\r\nn = 10000;\r\ns_correct = 35252550;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 100000;\r\ns_correct = 3522204030;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nn = 1000000;\r\ns_correct = 352218412502;\r\nassert(isequal(sumRadicals(n),s_correct))\r\n%%\r\nfiletext = fileread('sumRadicals.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-27T09:04:12.000Z","updated_at":"2026-04-08T13:04:36.000Z","published_at":"2021-09-27T10:53:42.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Radical_of_an_integer\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eradical of a positive integer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as the product of the distinct prime numbers dividing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For example, the distinct prime factors of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[2\\\\ 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, therefore the radical of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Similarly, the radicals of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e125\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1344\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, respectively, The number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis considered to be the radical of itself.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the sum of the radicals of all positive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\leq n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the radicals are: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1, 2, 3, 2, 5, 6, 7, 2, 3, 10]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe output should be \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e'41'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"},{"id":52814,"title":"Easy Sequences 27: Product of Radicals of Integers","description":"The radical of a positive integer  is defined as the product of the distinct prime numbers dividing . For example, the distinct prime factors of  is , therefore the radical of  is . Similarly, the radicals of ,  and  are ,  and , respectively, The numberis considered to be the radical of itself.\r\nGiven a limit , find the product of the radicals of all positive integers . Since, the radical product can get huge fast, please output only the number of digits of the product.\r\nFor , the radicals are: , their product is . Therefore, the output should be '6' digits","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 144px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 72px; transform-origin: 407px 72px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eThe \u003c/span\u003e\u003c/span\u003e\u003ca target='_blank' href = \"https://en.wikipedia.org/wiki/Radical_of_an_integer\"\u003e\u003cspan style=\"\"\u003e\u003cspan style=\"\"\u003eradical of a positive integer\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201px 8px; transform-origin: 201px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is defined as the product of the distinct prime numbers dividing \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003ex\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 59px 8px; transform-origin: 59px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. For example, the distinct prime factors of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 35.5px; height: 18.5px;\" width=\"35.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78px 8px; transform-origin: 78px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, therefore the radical of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADMAAAAkCAYAAAAkcgIJAAABYklEQVRYhe2XUbGDMBBFjwccxAAGqgAFOMBBHdQCGpCAh1pAAxb6PkgmGR4hu9n+NWeGjzJ7kr2Qpik0Go3GL+KArsJ5+Ktmvlr3dtAZ+AC90BmBDViAp/d3YKL8QCxulo4YIlySMMF5ne5P/v5605TFzTJwPJUBeCMPEybdMpOumWatrpgnsjAdx3K4m3DMjGVxVUjDTEndkKlxSU3atMVVIQ2TLkd3UxfewPYlV4U0TKjZC+Ot/G/c4qqQhOkrGxqMrhpJmEdlQ5PRVaMNsyjGO4fRumq0YdbCeC/yYbSump9bZlQ2FMazuCqkYTZlQztxe7W4KqRhZmFdqHl/yVUhDZOu/TFTk/6mpGve4qqQhoG4DHK7UtiNrk7GFleMJowjnp/OtenJ+Orfo8UV4Yhfzg9HsBK9n3hPmnLEw+TdMcTiZnEcr3W9uGbKa7bzNYt3Fv9ZsgNZ3Eaj0Wg0GiX+AJDSC8VPsu1pAAAAAElFTkSuQmCC\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9px 8px; transform-origin: 9px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAABJUlEQVRYhe2WbRGEIBCGnw42oIAFTGACG9jABlYwgxHocBXMYAXvh3ByzqGwfowzxzvDD5nd5WGXFSApKelZUkAm8CnMOBWkAyYgD/SpgAHogcb4j0BN/KY+yhwQO0KArE+7mq/NvJZAlcw7K4FXBJBddPAsqj2wUWoCgTLmsmwtWAXGOgWoduxKj41ybMRZCgVyS6s27GwWh6uBrM24E08TBn4IKBcC+Up7GKgQAtV3APUR8W4B0jvx2ruBHlEyhECin2Mo0BAJNHJh28P3RRySyZcEJgbIPUeVx8b9X4nOTwwQLOXwdZrtMN9r4HQgxXJXrW3d14D4BalYDutk4PaUm4VHB0qxXL6i60Ixp1f/GB379c+MTW98evMt6qqkpKSkv9UbptKi8sNv99EAAAAASUVORK5CYII=\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 80px 8px; transform-origin: 80px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Similarly, the radicals of \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25.5px; height: 18px;\" width=\"25.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEIAAAAkCAYAAAA9+eyvAAAB4ElEQVRoge2YbZGEMAyGHw84wMAaQAEK1gEOcICF1YAEPGDhNGDh7kebocvwkZDu3N1Mn5n+2e3bkJeQFqBQKBQKhU9RA5VR8wCaqPVQxXWs8b3aN2rgBXwTEtMEfgFL1Mj4ihd0h9kQP6cWWBNKk7larIqBF2AAemDcrGE1ozfEz6kFoI2LtKyOahabCOZty/DBWiGT4ToabDcil3YXrasN4e4fIdW1KONWcW5aUdpkPNpDtEa0nDdFWWdWxh0J1ZPeWW0yHu0h7ucsIhXRKeZ2hOZaY0/Goz0lhxFSqhPX25j0E2mqlmQ82ku8RshOMqLby2fCjiNYkvFoL7lrRAU8eT9PTJz3kYGQTGqYNhmPVsUdI2QHmRKtjIV9M5r43zaGJhmPVk2OHrGtjO02Kz1kr5FeJePRmsi1a9SsZiy8l/DI8RnkKhmP1kQuIyA8x9u1OoIxLeHCt6NLNM/k98qpNZPTiL07tNdHNOPh1Jr5hBHpMXsgJHQ00nedOfm9dmrN5DTiGdcZriYmeJ7zP9sjJsLx9+5b5L8wQhrh0QcYeddojfH/hBE1ITFZrD+Zu/2IM8X5PesR+87F/KoRZ43oxf7hRbazdO4Qf/N8s5Td4U6T82gLhUKhUCgUClp+ANDXK1nbeFY7AAAAAElFTkSuQmCC\" style=\"width: 33px; height: 18px;\" width=\"33\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.5px 8px; transform-origin: 14.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e are \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAkCAYAAADhAJiYAAAA6klEQVRYhe2VWxGDMBBFj4c4wAAGogAFdRAHOMACGpCAByxUQy20Hwl0y0BLk5ZlhtyZ/UgmXM5uHgtZWVnHUgGYhO8NYBM9JpAWuANlgs+Q6mEEyBixZnWqRxVMKp6ZxZpZfpPUpJTsDHADuqMAdUDPa5XUgBxwxV8KdaASv1U2jNWBBqARY1WgJgDJB1ANyOK3ar5OBWi84m4FdHegLsSSdgdy+OpU4efzcMLjIuajGu0WoF6s+SaiqrUFqAlQayH74SDmi38BfZL6w3geoALfIEezWguoYP2gtiw/fu9UkniQs7Kysk6pB0ucjplAUbTSAAAAAElFTkSuQmCC\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 4px 8px; transform-origin: 4px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e5\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 16px 8px; transform-origin: 16px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e and \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 18px; height: 18px;\" width=\"18\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 83.5px 8px; transform-origin: 83.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, respectively, The number\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: normal; font-weight: 400; color: rgb(0, 0, 0);\"\u003e1\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 121.5px 8px; transform-origin: 121.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eis considered to be the radical of itself.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 45.5px 8px; transform-origin: 45.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003eGiven a limit \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"font-family: \u0026quot;STIXGeneral\u0026quot;, \u0026quot;STIXGeneral-webfont\u0026quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);\"\u003en\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 195.5px 8px; transform-origin: 195.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e, find the product of the radicals of all positive integers \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 25px; height: 18px;\" width=\"25\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 2px 8px; transform-origin: 2px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; \"\u003e.\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 110px 8px; transform-origin: 110px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e Since, the radical product can get huge fast, please output only the number of digits of the product.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 13px 8px; transform-origin: 13px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 44px; height: 18px;\" width=\"44\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 57px 8px; transform-origin: 57px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, the radicals are: \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 152.5px; height: 18.5px;\" width=\"152.5\" height=\"18.5\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 53px 8px; transform-origin: 53px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e, their product is \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"vertical-align:-5px\"\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 54.5px; height: 18px;\" width=\"54.5\" height=\"18\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 39.5px 8px; transform-origin: 39.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e. Therefore, \u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 68.5px 8px; transform-origin: 68.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"text-decoration: underline; text-decoration-line: underline; \"\u003ethe output should be '\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 5.5px 8px; transform-origin: 5.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"font-weight: 700; text-decoration: underline; text-decoration-line: underline; \"\u003e6'\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 18.5px 8px; transform-origin: 18.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003e digits\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function r = prodRadicals(n)\r\n    r = 6;\r\nend","test_suite":"%%\r\nn = 10;\r\nr_correct = 6;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nn = 1000;\r\nr_correct = 2263;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nns = 10000:50000;\r\nrs = arrayfun(@(n) prodRadicals(n),ns);\r\nss_correct = [4503407257 70876 91001 111568 132490 153727 175243 196990 47696];\r\nassert(isequal([sum(rs) rs(10000:5000:40000) floor(std(rs))],ss_correct))\r\n%%\r\nn = 1000000;\r\nr_correct = 5238328;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nn = 1000000000;\r\nr_correct = 8237674403;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nn = intmax;\r\nr_correct = 18403071064;\r\nassert(isequal(prodRadicals(n),r_correct))\r\n%%\r\nfiletext = fileread('prodRadicals.m');\r\nnot_allowed = contains(filetext, 'persistent') || contains(filetext, 'global') || contains(filetext, 'BigInteger') || contains(filetext, 'java'); \r\nassert(~not_allowed)","published":true,"deleted":false,"likes_count":2,"comments_count":0,"created_by":255988,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":10,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2021-09-27T09:04:14.000Z","updated_at":"2026-04-22T13:56:23.000Z","published_at":"2021-09-27T10:28:34.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eThe \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:hyperlink w:docLocation=\\\"https://en.wikipedia.org/wiki/Radical_of_an_integer\\\"\u003e\u003cw:r\u003e\u003cw:t\u003eradical of a positive integer\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is defined as the product of the distinct prime numbers dividing \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003ex\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. For example, the distinct prime factors of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[2\\\\ 5]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, therefore the radical of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e100\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Similarly, the radicals of \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e125\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1344\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e are \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e14\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e5\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e and \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e42\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, respectively, The number\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003eis considered to be the radical of itself.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003eGiven a limit \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e, find the product of the radicals of all positive integers \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e\\\\leq n\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e.\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e Since, the radical product can get huge fast, please output only the number of digits of the product.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003en = 10\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, the radicals are: \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e[1, 2, 3, 2, 5, 6, 7, 2, 3, 10]\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e, their product is \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"false\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e151,200\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e. Therefore, \u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003ethe output should be '\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:rPr\u003e\u003cw:b/\u003e\u003cw:u/\u003e\u003c/w:rPr\u003e\u003cw:t\u003e6'\u003c/w:t\u003e\u003c/w:r\u003e\u003cw:r\u003e\u003cw:t\u003e digits\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"group:\"Easy Sequences Volume II\" 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