A356541 a(n) = Sum_{d|n} d * (d!)^(n/d-1).

1, 3, 4, 9, 6, 33, 8, 121, 118, 643, 12, 7349, 14, 35423, 75904, 378129, 18, 6400179, 20, 46256149, 177951190, 439086871, 24, 21025820825, 1036800026, 80951278619, 1185142088476, 2117428953117, 30, 153033887545887, 32, 859169550303265, 17526860326038562

Offset

1,2

Links

Table of n, a(n) for n=1..33.

Formula

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

If p is prime, a(p) = 1 + p.

Mathematica

a[n_] := DivisorSum[n, # * (#)!^(n/# - 1) &]; Array[a, 33] (* Amiram Eldar, Aug 30 2023 *)

Prog

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

Crossrefs

Cf. A356542, A356543.

Sequence in context: A054791 A167531 A344195 * A062319 A285265 A330385

Adjacent sequences: A356538 A356539 A356540 * A356542 A356543 A356544

Keyword

nonn

Author

Seiichi Manyama, Aug 11 2022

Status

approved