A358595 a(n) = n! * Sum_{d|n} d^n / d!^(n/d).

1, 6, 33, 376, 3245, 67716, 828583, 22050176, 420850809, 12580687900, 285351587411, 11736333558720, 302881333613053, 13450914411140584, 463402585399165875, 22345557703564558336, 827240617573764860177, 48442529220731147887020

Offset

1,2

Links

Table of n, a(n) for n=1..18.

Formula

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

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

Mathematica

a[n_] := n! * DivisorSum[n, #^n / #!^(n/#) &]; Array[a, 20] (* Amiram Eldar, Jul 31 2023 *)

Prog

(PARI) a(n) = n!*sumdiv(n, d, d^n/d!^(n/d));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, (k*x)^k/(k!-(k*x)^k))))

Crossrefs

Cf. A354890, A358593.

Sequence in context: A343567 A306182 A354888 * A121376 A354890 A046707

Adjacent sequences: A358592 A358593 A358594 * A358596 A358597 A358598

Keyword

nonn

Author

Seiichi Manyama, Feb 23 2023

Status

approved