OFFSET
0,3
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..100
FORMULA
G.f.: Sum_{m>0} m!*x^m/(1-x^m). - Vladeta Jovovic, Aug 06 2004
Inverse Moebius transform of factorials (A000142). - Jonathan Vos Post, Mar 19 2006
a(n) ~ n!. - Vaclav Kotesovec, Mar 14 2015
L.g.f.: -log(Product_{k>=1} (1 - x^k)^((k-1)!)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 23 2018
EXAMPLE
The divisors of 3 are 1 and 3 so 1! + 3! = 7. The divisors of 4 are 1, 2 and 4 so 1! + 2! + 4! = 27.
MATHEMATICA
nmax=20; CoefficientList[Series[Sum[m!*x^m/(1-x^m), {m, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 14 2015 *)
Join[{0}, Table[Total[Divisors[n]!], {n, 20}]] (* Harvey P. Dale, Aug 15 2024 *)
PROG
(PARI) a(n)=if(n<1, 0, sumdiv(n, d, d!));
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Jul 07 2001
STATUS
approved