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%I #8 Nov 09 2019 15:38:48
%S 1,3,280,2627625,5194672859376,5150805819130303332,
%T 1461034854396267778567973305958400,
%U 450538787986875167583433232345723106006796340625,146413934927214422927834111686633731590253260933067148964500000000
%N a(n) is the least integer of the form (n^2)!/(n!)^k.
%C (n^2)!/(n!)^(n+1) is an integer for every n (see A057599). Hence k >= n+1. Conjecture: k=n+1 only when n is prime or a power of a prime.
%H Andrew Howroyd, <a href="/A096126/b096126.txt">Table of n, a(n) for n = 1..25</a>
%e a(4) = 16!/(4!)^5 = 2627625 which is not further divisible by 24.
%o (PARI) a(n)={if(n==1, 1, (n^2)!/(n!^valuation((n^2)!,n!)))} \\ _Andrew Howroyd_, Nov 09 2019
%Y Cf. A034841, A057599, A096127.
%K nonn
%O 1,2
%A _Amarnath Murthy_, Jul 03 2004
%E Edited by _Don Reble_, Jul 04 2004
%E a(9) from _Andrew Howroyd_, Nov 09 2019