A356010 a(n) = n! * Sum_{k=1..n} floor(n/k)/k.

1, 5, 23, 134, 814, 6324, 50028, 475824, 4806576, 54597600, 644119200, 8847100800, 121718332800, 1853505158400, 29894856364800, 518855607244800, 9197155541145600, 179420609436364800, 3537039053405491200, 75849875285280768000, 1670700245252548608000

Offset: 1

Author

Seiichi Manyama, Jul 23 2022

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..447

Crossrefs

Cf. A038048, A355886.

Programs

Maple

S:= ListTools:-PartialSums([seq(numtheory:-sigma(k)/k, k=1..30)]):
seq(n! * S[n], n=1..30); # Robert Israel, Aug 10 2025

PARI

a(n) = n!*sum(k=1, n, n\k/k);

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(k*(1-x^k)))/(1-x)))

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-x^k))/(1-x)))

PARI

a(n) = n!*sum(k=1, n, sigma(k)/k); \\ Seiichi Manyama, Aug 03 2022

Formula

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

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

a(n) ~ c * n! * n, where c = Pi^2/6. - Vaclav Kotesovec, Aug 02 2022

a(n) = n! * Sum_{k=1..n} sigma(k)/k. - Seiichi Manyama, Aug 03 2022