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

1,2

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A000142, A027423, A010553.

Sequence in context: A329576 A101137 A256386 * A122700 A048486 A179402

Adjacent sequences: A053018 A053019 A053020 * A053022 A053023 A053024

Keyword

nonn

Author

Labos Elemer, Feb 24 2000

Status

approved