A153824 Sum of proper divisors of n!: a(n) = sigma(n!) - n!.

0, 0, 1, 6, 36, 240, 1698, 14304, 118800, 1118160, 11705288, 144092256, 1738439808, 24817158912, 355309325280, 5378578601760, 86081749397280, 1570394279039040, 28281459220193088, 572031558109589760, 11458497230555094720

Offset: 0

Author

Omar E. Pol, Jan 02 2009

Keywords

• nonn

Comments

a(n) is the sum of proper divisors of factorial number A000142(n).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A000142, A000203, A001065, A062569.

Programs

Magma

[DivisorSigma(1,Factorial(n)) - Factorial(n): n in [0..20]]; // Vincenzo Librandi, Aug 31 2016

Maple

with(numtheory): seq(sigma(factorial(n))-factorial(n), n = 0 .. 22); # Emeric Deutsch, Jan 07 2009

Mathematica

Table[DivisorSigma[1, n!] - n!, {n, 0, 50}] (* G. C. Greubel, Aug 30 2016 *)

PARI

a(n) = sigma(n!) - n!; \\ Michel Marcus, Aug 31 2016

Formula

a(n) = A000203(n!) - n! = A062569(n) - A000142(n) = A001065(A000142(n)).

Extensions

Extended by Emeric Deutsch, Jan 07 2009