A354900 a(n) = n! * Sum_{d|n} d^d / (n/d)!.

1, 9, 163, 6193, 375001, 33602521, 4150656721, 676462516801, 140587148681281, 36288005670120961, 11388728893445164801, 4270826391670469473921, 1886009588552176549862401, 968725766890781857146309121, 572622616354852243874626732801

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Formula

E.g.f.: Sum_{k>0} k^k * (exp(x^k) - 1).

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

Mathematica

a[n_] := n! * DivisorSum[n, #^#/(n/#)! &]; Array[a, 15] (* Amiram Eldar, Jun 11 2022 *)

Prog

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

Crossrefs

Cf. A057625, A354843, A354888, A354892, A354899.

Sequence in context: A041147 A041144 A212334 * A354892 A086759 A053130

Adjacent sequences: A354897 A354898 A354899 * A354901 A354902 A354903

Keyword

nonn

Author

Seiichi Manyama, Jun 11 2022

Status

approved