A345465 a(n) = Sum_{d|n} (d!)^d.
1, 5, 217, 331781, 24883200001, 139314069504000221, 82606411253903523840000001, 6984964247141514123629140377600331781, 109110688415571316480344899355894085582848000000217, 395940866122425193243875570782668457763038822400000000024883200005
Offset: 1
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..30
Programs
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Mathematica
Total/@Table[((Divisors[n])!)^Divisors[n],{n,10}] (* Harvey P. Dale, Apr 24 2022 *) -
PARI
a(n) = sumdiv(n, d, d!^d);
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PARI
my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k!*x)^k/(1-x^k)))
Formula
G.f.: Sum_{k >= 1} (k! * x)^k/(1 - x^k).
If p is prime, a(p) = 1 + (p!)^p.