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