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A346196
a(n) = Sum_{d|n} (d!)^n.
3
1, 5, 217, 331793, 24883200001, 139314069504046721, 82606411253903523840000001, 6984964247141514123629140487675314433, 109110688415571316480344899355894085582848010077697, 395940866122425193243875570782668457763038823019173642240000001025
OFFSET
1,2
LINKS
FORMULA
G.f.: Sum_{k >= 1} (k! * x)^k/(1 - (k! * x)^k).
If p is prime, a(p) = 1 + (p!)^p.
MATHEMATICA
a[n_] := DivisorSum[n, (#!)^n &]; Array[a, 10] (* Amiram Eldar, Aug 30 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, d!^n);
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k!*x)^k/(1-(k!*x)^k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 10 2021
STATUS
approved