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, 51090942171709445047, 1124000727777647596803
Offset: 0
Examples
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.
Links
- Harry J. Smith, Table of n, a(n) for n = 0..100
Programs
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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 *) -
PARI
a(n)=if(n<1, 0, sumdiv(n, d, d!));
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