Problem 51312. Count the square-full divisors of a number

Created by ChrisR

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<div 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; "><div style="block-size: 93px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 46.5px; transform-origin: 407px 46.5px; vertical-align: baseline; "><div 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; "><span 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: 325.775px 7.91667px; transform-origin: 325.775px 7.91667px; unicode-bidi: normal; "><span style="">A square-full number has a prime factorization in which all exponents are 2 or greater. For example, 72 = </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAE4AAAAnCAYAAAChUX6PAAACVUlEQVRoge2ZYZHCMBBGn4c6qIEaqAIU1EEd4KAWqgEJeMACGrDA/Ui+Sa6XlBSalJvJm8kwB3fNstn9drMHlUqlUtlKB5ztOh1sy1Z6nO19yY1n4AFc7esTuJQ04E0a4Abc7esTZ3uTe/NhsVFjDXliovCbuQKj93OHO/hz7s3nwHtnu/k3p2yLibIlI8b20GfZmTAn9820hDOi503HDZgQVr4/MKmYmnZK1aIia5FsKN3umIzYoldy3JT6Bw2/HRZar1Kvt8be7ZcoyYyLFL9I6fDbxOdIZpL1Wek1YxzQY/JdQq8Ve+DJbur/fqmomzAOW+4nvXoS1uIQdzZEm6pJLEouGw3Q6aca+wkS+Vg6yvYUzVWgJDOz/iVbnONSH6zeKDcj65Gt1Htld8f6AQS58Tqn1SCmVsurXUcz8Vrs1QhnkRYVjtQoulGgiUxAxSpWHFQUQ07bpcAp4pYnNwQ27dlWyXIxY5wSyyZF2hj4bGSHg29wabo0wr/fnXB94JHXrRaXIQ/iDvCLXmh9fPADcZ1ocZOFkWMd1hPvRZcS409zQmuXNJVO5J4YDITT5h16XFukldyf7YGa2tyRpLZh75HUyXtusfuzRL7E9cnXm01NaAJ+5GWXko6yd07tl2NPP+qyOq6003KjiceDjDqd4rTsY+WdUcRlG+evNYQ+F46Zt72L/ieSZSItp+nOFlsXDhorR1DDHRtYqgfNcv2T09a6aH/t1WvtgV+NdUvQIU8Y2clm7xanfcMd1Kfj79XpZt8b+H96XKlUKpVKpVKpVP41P0ab669BsHIHAAAAAElFTkSuQmCC" alt="2^3*3^2" style="width: 39px; height: 19.5px;" width="39" height="19.5"></span><span 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: 32.675px 7.91667px; transform-origin: 32.675px 7.91667px; unicode-bidi: normal; "><span style=""> is square-full, but 45 = </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" alt="3^2*5" style="width: 34px; height: 19.5px;" width="34" height="19.5"></span><span 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: 326.767px 7.91667px; transform-origin: 326.767px 7.91667px; unicode-bidi: normal; "><span style=""> is not. The number 1 is considered square-full. Therefore, 12 has two square-full divisors (1 and 4), while 48 has 4 (1, 4, 8, and 16). </span></span></div><div 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; "><span 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: 255.025px 7.91667px; transform-origin: 255.025px 7.91667px; unicode-bidi: normal; "><span style="">Write a function that returns the number of square-full divisors of the input number.</span></span></div></div></div>

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Dyuman Joshi on 25 May 2021

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Problem 51312. Count the square-full divisors of a number

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Problem 51312. Count the square-full divisors of a number

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