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A096127
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a(n) = largest k such that (n^2)!/(n!)^k is an integer.
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1
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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; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| Conjecture: a(n)=n+1 only when n is prime or a power of a prime.
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EXAMPLE
| a(6) = 8 as 36!/(6!)^8 is an integer which is not further divisible by 720.
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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)
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CROSSREFS
| Cf. A034841, A057599, A096126.
Sequence in context: A084919 A153100 A143152 * A112768 A197354 A089399
Adjacent sequences: A096124 A096125 A096126 * A096128 A096129 A096130
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 03 2004
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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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