id:A096127 - OEIS Search Results

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

+0
2

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 (list; graph; listen)

	OFFSET	`2,1`
	COMMENT	`Conjecture: a(n)=n+1 only when n is prime or a power of a prime.`
	EXAMPLE	`a(6) = 8 as 36!/(6!)^8 is an integer which is not further divisible by 720.`
	MATHEMATICA	`f[n_] := Block[{k = n}, While[ IntegerQ[(n^2)!/n!^k], k++ ]; k - 1]; Table[ f[n], {n, 75}] (from Robert G. Wilson v Jul 03 2004)`
	CROSSREFS	`Cf. A034841, A057599, A096126.` `Sequence in context: A084919 A153100 A143152 this_sequence A112768 A089399 A003619` `Adjacent sequences: A096124 A096125 A096126 this_sequence A096128 A096129 A096130`
	KEYWORD	`nonn`
	AUTHOR	`Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 03 2004`
	EXTENSIONS	`Edited by Don Reble (djr(AT)nk.ca) and Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 04 2004`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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