A345684 a(n) = n! * Sum_{k=1..n} k/floor(n/k).

1, 5, 32, 198, 1584, 12480, 122520, 1214640, 14011200, 166924800, 2274894720, 31135104000, 485667705600, 7710089587200, 133974352512000, 2386854434764800, 46621903994265600, 918384939343872000, 19760215067873280000, 430137075045629952000, 10042411264251125760000

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..448

Formula

a(n) ~ c * n^2 * n!, where c = Sum_{j>=1} (2*j + 1) / (2*j^3*(j+1)^2) = Pi^2/12 + zeta(3)/2 - 1 = 0.423495...

E.g.f.: -(1/(1-x)) * Sum_{k>0} k * (1 - x^k) * log(1 - x^k). - Seiichi Manyama, Jul 23 2022

Mathematica

Table[n!*Sum[k/Floor[n/k], {k, 1, n}], {n, 1, 25}]
Table[n!*Sum[(Floor[n/j] - Floor[n/(1 + j)])*((1 + Floor[n/j] + Floor[n/(1 + j)])/2/j), {j, 1, n}], {n, 1, 25}]

Prog

(PARI) a(n) = n!*sum(k=1, n, k/(n\k)); \\ Michel Marcus, Jun 23 2021
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, k*(1-x^k)*log(1-x^k))/(1-x))) \\ Seiichi Manyama, Jul 23 2022

Crossrefs

Cf. A006218, A010786, A076000, A092143, A117871, A345682, A345683.

Sequence in context: A270565 A271165 A015541 * A297068 A024064 A164594

Adjacent sequences: A345681 A345682 A345683 * A345685 A345686 A345687

Keyword

nonn

Author

Vaclav Kotesovec, Jun 23 2021

Status

approved