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A345465 a(n) = Sum_{d|n} (d!)^d. 3

%I

%S 1,5,217,331781,24883200001,139314069504000221,

%T 82606411253903523840000001,6984964247141514123629140377600331781,

%U 109110688415571316480344899355894085582848000000217,395940866122425193243875570782668457763038822400000000024883200005

%N a(n) = Sum_{d|n} (d!)^d.

%H Seiichi Manyama, <a href="/A345465/b345465.txt">Table of n, a(n) for n = 1..30</a>

%F G.f.: Sum_{k >= 1} (k! * x)^k/(1 - x^k).

%F If p is prime, a(p) = 1 + (p!)^p.

%o (PARI) a(n) = sumdiv(n, d, d!^d);

%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k!*x)^k/(1-x^k)))

%Y Cf. A036739, A062796, A217576, A346196, A348146.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jul 10 2021

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Last modified January 27 09:44 EST 2022. Contains 350607 sequences. (Running on oeis4.)