A356661 a(n) = n! * Sum_{d|n} 1/d^(n/d - 1).

1, 4, 12, 60, 240, 1860, 10080, 95760, 766080, 8210160, 79833600, 1100484000, 12454041600, 188172784800, 2683799838720, 44951306400000, 711374856192000, 13745322470880000, 243290200817664000, 5142812718440517120, 103294640229580800000, 2351280996859354560000

Offset

1,2

Links

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

Formula

a(p) = 2 * p! for prime p.

E.g.f.: Sum_{k>=1} x^k/(1 - x^k/k).

Mathematica

a[n_] := n! * DivisorSum[n, 1/#^(n/# - 1) &]; Array[a, 22] (* Amiram Eldar, Aug 21 2022 *)

Prog

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

Crossrefs

Cf. A087905, A087909, A098558, A356662.

Sequence in context: A057394 A054719 A356662 * A351286 A335656 A355268

Adjacent sequences: A356658 A356659 A356660 * A356662 A356663 A356664

Keyword

nonn

Author

Seiichi Manyama, Aug 21 2022

Status

approved