A053023 Divisor function applied thrice to n!.

1, 2, 2, 3, 2, 4, 6, 6, 6, 5, 8, 8, 8, 8, 8, 9, 8, 10, 8, 10, 10, 12, 10, 10, 10, 15, 16, 16, 18, 16, 8, 16, 10, 12, 16, 18, 14, 3, 14, 16, 24, 16, 16, 20, 24, 24, 28, 24, 24, 16, 24, 24, 32, 32, 28, 32, 18, 20, 24, 28, 36, 32, 36, 24, 21, 24, 20, 40, 40, 30, 30, 36, 40, 42, 24, 32

Offset: 1

Author

Labos Elemer, Feb 24 2000

Keywords

• nonn

Examples

			A036450(x) = 8 if x = 11!, 12!, 13!, 14!, 15!. The reversed sequences of these d-iterates are {2, 3, 4, 8, 24, 540, 39916800}, {2, 3, 4, 8, 24, 792, 479001600}, {2, 3, 4, 8, 30, 1584, 6227020800}, {2, 3, 4, 8, 30, 2592, 87178291200}, {2, 3, 4, 8, 42, 4032, 1307674368000}.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000142, A010553, A036450, A053021.

Programs

Mathematica

a[n_] := Nest[DivisorSigma[0, #]&, n!, 3]; Array[a, 100] (* Amiram Eldar, Aug 12 2024 *)

PARI

a(n) = numdiv(numdiv(numdiv(n!))); \\ Amiram Eldar, Aug 12 2024

Formula

a(n) = d(d(d(n!))) = A036450(A000142(n)) = A036450(n!).