Factorial : Definition

a(1) = 1; for n > 1, a(n) is defined by the property that n^a(n) divides n! but n^(a(n)+1) does not.

a(n) = least k>1 such that k^n divides k!

Numbers n where A011776(n) grows

Prove that the value of [N!/((N+1)(N+2))] is always even, for any given positive integer N

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