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

0,3

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

Links

Amiram Eldar, Table of n, a(n) for n = 0..1000

Formula

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

Mathematica

a[n_] := DivisorSigma[0, n!^n]; Array[a, 25, 0] (* Amiram Eldar, Mar 11 2026 *)

Prog

(PARI) a(n) = numdiv((n!)^n);

Crossrefs

Cf. A000005, A027423, A036740.

Sequence in context: A247363 A007143 A359176 * A293579 A044046 A179600

Adjacent sequences: A062957 A062958 A062959 * A062961 A062962 A062963

Keyword

easy,nonn

Author

Jason Earls, Jul 22 2001

Status

approved