cp's OEIS Frontend

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

%I A345684 #19 Jul 23 2022 09:53:53
%S A345684 1,5,32,198,1584,12480,122520,1214640,14011200,166924800,2274894720,
%T A345684 31135104000,485667705600,7710089587200,133974352512000,
%U A345684 2386854434764800,46621903994265600,918384939343872000,19760215067873280000,430137075045629952000,10042411264251125760000
%N A345684 a(n) = n! * Sum_{k=1..n} k/floor(n/k).
%H A345684 Seiichi Manyama, <a href="/A345684/b345684.txt">Table of n, a(n) for n = 1..448</a>
%F A345684 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...
%F A345684 E.g.f.: -(1/(1-x)) * Sum_{k>0} k * (1 - x^k) * log(1 - x^k). - _Seiichi Manyama_, Jul 23 2022
%t A345684 Table[n!*Sum[k/Floor[n/k], {k, 1, n}], {n, 1, 25}]
%t A345684 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}]
%o A345684 (PARI) a(n) = n!*sum(k=1, n, k/(n\k)); \\ _Michel Marcus_, Jun 23 2021
%o A345684 (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
%Y A345684 Cf. A006218, A010786, A076000, A092143, A117871, A345682, A345683.
%K A345684 nonn
%O A345684 1,2
%A A345684 _Vaclav Kotesovec_, Jun 23 2021