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Non-divisibility of factorials (Posted on 2024-10-16)

For what values of n is

(n²-1)!

not divisible by

(n!)ⁿ ?

No Solution Yet Submitted by Jer

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exploration as far as possible

| Comment 1 of 2

clc

for n=sym(1:31)

a=factorial(n^2-1);

b=factorial(n)^n;

if mod(a,b)>0

fprintf('%d,',n)

end

% disp(' ')

end

finds

2,3,4,5,7,11,13,17,19,23,29,31

Going beyond n=31 goes outside Matlab's factorial capability.

The OEIS identifies the sequence as

A175787, the primes together with 4.

Posted by Charlie on 2024-10-16 18:05:31

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