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A062960
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Number of divisors of (n!)^n (A036740).
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0
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1, 1, 3, 16, 65, 576, 2275, 27840, 78489, 236800, 767151, 13264560, 31184725, 640564848, 2082421125, 5514535936, 10924376001, 279876280320, 584912713825, 16888996800000, 37538691697521, 91766133606400, 272224952406045
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Divisible by n+1. Proof: Exponent of largest prime dividing n! in prime factorization of n! is 1, i.e., n! = p_1^e_1*p_2^e_2*...*p_(s-1)^e_(s-1)*p_s, p_1<p_2<....<p_(s-1)<p_s. Thus tau(n!^n) = (n*e_1+1)*(n*e_2+1)*...*(n*e_(s-1)+1)*(n+1). - Vladeta Jovovic Oct 01 2004
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PROG
| (PARI) for(n=0, 22, print(numdiv((n!)^n)))
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CROSSREFS
| Sequence in context: A155160 A037451 A007143 * A044046 A179600 A000269
Adjacent sequences: A062957 A062958 A062959 * A062961 A062962 A062963
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KEYWORD
| easy,nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Jul 22 2001
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