A356543 a(n) = Sum_{d|n} (d!)^(n/d-1).

1, 2, 2, 4, 2, 12, 2, 34, 38, 138, 2, 1546, 2, 5106, 15698, 54274, 2, 889314, 2, 5689090, 25448258, 39917826, 2, 2486196610, 207360002, 6227024898, 131683574018, 215393466370, 2, 14769495662082, 2, 86475697160194, 1593350982706178, 355687428161538, 648227266560002

Offset: 1

Author

Seiichi Manyama, Aug 11 2022

Keywords

• nonn

Crossrefs

Cf. A087909, A342628, A356541.

Programs

Mathematica

a[n_] := DivisorSum[n, (#)!^(n/# - 1) &]; Array[a, 35] (* Amiram Eldar, Aug 30 2023 *)

PARI

a(n) = sumdiv(n, d, d!^(n/d-1));

PARI

my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-k!*x^k)))

Formula

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

If p is prime, a(p) = 2.