A358279 a(n) = Sum_{d|n} (d-1)! * d^(n/d).

1, 3, 7, 29, 121, 747, 5041, 40433, 362935, 3629433, 39916801, 479006531, 6227020801, 87178326609, 1307674371487, 20922790212353, 355687428096001, 6402373709021811, 121645100408832001, 2432902008212950169, 51090942171709691335, 1124000727778046766849

Offset

1,2

Links

Table of n, a(n) for n=1..22.

Formula

G.f.: Sum_{k>0} k! * x^k/(1 - k * x^k).

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

Mathematica

a[n_] := DivisorSum[n, (# - 1)! * #^(n/#) &]; Array[a, 22] (* Amiram Eldar, Aug 30 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (d-1)!*d^(n/d));
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k!*x^k/(1-k*x^k)))

Crossrefs

Cf. A038507, A062363, A078308, A217576, A321521, A358280.

Sequence in context: A088095 A333392 A358389 * A217576 A173280 A141477

Adjacent sequences: A358276 A358277 A358278 * A358280 A358281 A358282

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 08 2022

Status

approved