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%I #13 Apr 06 2021 03:39:07
%S 3,4,5,6,8,8,9,10,12,12,14,14,16,18,17,18,20,20,22,24,24,24,26,26,28,
%T 28,30,30,32,32,33,35,36,38,38,38,40,42,42,42,44,44,46,48,48,48,50,50,
%U 52,54,55,54,56,58,58,60,60,60,62,62,64,66,65,67,68,68,70,72,73,72,74,74
%N a(n) is the largest k such that (n^2)!/(n!)^k is an integer.
%C Conjecture: a(n)=n+1 only when n is prime or a power of a prime. [Verified for n=2..5000. - _Amiram Eldar_, Apr 06 2021]
%H Amiram Eldar, <a href="/A096127/b096127.txt">Table of n, a(n) for n = 2..5000</a>
%e a(6) = 8 as 36!/(6!)^8 is an integer which is not further divisible by 720.
%t f[n_] := Block[{k = n}, While[ IntegerQ[(n^2)!/n!^k], k++ ]; k - 1]; Table[ f[n], {n, 75}] (* _Robert G. Wilson v_, Jul 03 2004 *)
%Y Cf. A034841, A057599, A096126.
%K nonn
%O 2,1
%A _Amarnath Murthy_, Jul 03 2004
%E Edited by _Don Reble_ and _Robert G. Wilson v_, Jul 04 2004
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