given a natural number N, find a natural number n such that max ((n!)^2 <=N)

Help me out! given a natural number N, find a natural number n such that max ((n!)^2 <=N).

[Roger Wohlwend]

The term max((n!)^2 <=N) does not make sense. ((n!)^2 <=N is a Logical.

[Christiana Won]

I actually want to find the maimum value of n such that (n^2)!<= N

Answer 1

[Thorsten]

 N = 1400; 
 n = 1; 
 while prod(1:n)^2 < N
   n = n + 1; 
 end; 
 n = n - 1

[Torsten]

Better take "log" on both sides:

 N = 1400; 
 logN = log(N);
 n = 1; 
 while 2*sum(log(1:n)) < logN
   n = n + 1; 
 end; 
 n = n - 1

Best wishes

Torsten.

[Thorsten]

Good point. This allows one to run the code for higher N > 99.