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 A096127 a(n) = largest k such that (n^2)!/(n!)^k is an integer. 2

%I

%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) = 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.

%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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Last modified December 8 14:38 EST 2019. Contains 329865 sequences. (Running on oeis4.)