A356297 a(n) = n! * Sum_{k=1..n} sigma_0(k)/k.

1, 4, 16, 82, 458, 3228, 24036, 212448, 2032992, 21781440, 246853440, 3201742080, 42580650240, 621037186560, 9664270963200, 161166707251200, 2781679603046400, 52204357423411200, 1004687538456268800, 20823621371578368000, 447027656835852288000

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Formula

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

a(n) ~ n! * (log(n)^2/2 + 2*gamma*log(n) + gamma^2 - 2*sg1), where gamma is the Euler-Mascheroni constant A001620 and sg1 is the first Stieltjes constant (see A082633). - Vaclav Kotesovec, Aug 07 2022

Mathematica

Table[n! * Sum[DivisorSigma[0, k]/k, {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Aug 07 2022 *)

Prog

(PARI) a(n) = n!*sum(k=1, n, sigma(k, 0)/k);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-x^k)/k)/(1-x)))

Crossrefs

Cf. A000005, A006218, A356010, A356298, A356323.

Sequence in context: A110378 A076997 A092304 * A204066 A351816 A022564

Adjacent sequences: A356294 A356295 A356296 * A356298 A356299 A356300

Keyword

nonn

Author

Seiichi Manyama, Aug 03 2022

Status

approved