A062960 Number of divisors of (n!)^n (A036740).

1, 1, 3, 16, 65, 576, 2275, 27840, 78489, 236800, 767151, 13264560, 31184725, 640564848, 2082421125, 5514535936, 10924376001, 279876280320, 584912713825, 16888996800000, 37538691697521, 91766133606400, 272224952406045, 9248286151802880, 17279191734765625

Offset: 0

Author

Jason Earls, Jul 22 2001

Keywords

• easy
• nonn

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_1Vladeta Jovovic, Oct 01 2004

Crossrefs

Cf. A000005, A027423, A036740.

Programs

PARI

for(n=0,22,print(numdiv((n!)^n)))

Formula

a(n) = A000005(A036740(n)).