A062363 a(n) = Sum_{d|n} d!.

0, 1, 3, 7, 27, 121, 729, 5041, 40347, 362887, 3628923, 39916801, 479002353, 6227020801, 87178296243, 1307674368127, 20922789928347, 355687428096001, 6402373706091609, 121645100408832001, 2432902008180268947

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 *)

Prog

(PARI) a(n)=if(n<1, 0, sumdiv(n, d, d!));

Crossrefs

Cf. A000142, A179327.

Sequence in context: A347639 A350751 A062795 * A333362 A242328 A136580

Adjacent sequences: A062360 A062361 A062362 * A062364 A062365 A062366

Keyword

easy,nonn

Author

Jason Earls, Jul 07 2001

Status

approved