A053021 Number of divisors function applied twice to n!.

1, 2, 3, 4, 5, 8, 12, 12, 12, 16, 24, 24, 30, 30, 42, 36, 40, 48, 56, 80, 48, 72, 80, 112, 112, 144, 120, 216, 252, 168, 189, 168, 80, 224, 168, 288, 320, 121, 192, 440, 480, 384, 408, 624, 792, 864, 960, 1152, 864, 728, 504, 780, 840, 1080, 960, 840, 972

Offset: 1

Author

Labos Elemer, Feb 24 2000

Keywords

• nonn

Examples

			a(7) = d(d(7!)) = d(60) = 12;
a(8) = d(d(8!)) = d(96) = 12.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000142, A027423, A010553.

Programs

Mathematica

DivisorSigma[0,DivisorSigma[0,Range[60]!]] (* Harvey P. Dale, May 20 2013 *)

PARI

a(n) = numdiv(numdiv(n!)); \\ Michel Marcus, May 01 2016

Formula

a(n) = A010553(n!) = A000005(A027423(n)) = A000005(A000005(A000142(n))).