A053023 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

FORMULA

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

EXAMPLE

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}.

MATHEMATICA

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

PROG

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

CROSSREFS

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

Sequence in context: A239471 A241509 A268327 * A153725 A102247 A054249

Adjacent sequences: A053020 A053021 A053022 * A053024 A053025 A053026

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 24 2000

STATUS

approved