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

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, 28, 30, 30, 32, 32, 33, 35, 36, 38, 38, 38, 40, 42, 42, 42, 44, 44, 46, 48, 48, 48, 50, 50, 52, 54, 55, 54, 56, 58, 58, 60, 60, 60, 62, 62, 64, 66, 65, 67, 68, 68, 70, 72, 73, 72, 74, 74

Offset: 2

Author

Amarnath Murthy, Jul 03 2004

Keywords

• nonn

Comments

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]

Examples

			a(6) = 8 as 36!/(6!)^8 is an integer which is not further divisible by 720.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 2..5000

Crossrefs

Cf. A034841, A057599, A096126.

Programs

Mathematica

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 *)

Extensions

Edited by Don Reble and Robert G. Wilson v, Jul 04 2004