This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A356010 #21 Aug 11 2025 10:30:22
%S A356010 1,5,23,134,814,6324,50028,475824,4806576,54597600,644119200,
%T A356010 8847100800,121718332800,1853505158400,29894856364800,518855607244800,
%U A356010 9197155541145600,179420609436364800,3537039053405491200,75849875285280768000,1670700245252548608000
%N A356010 a(n) = n! * Sum_{k=1..n} floor(n/k)/k.
%H A356010 Robert Israel, <a href="/A356010/b356010.txt">Table of n, a(n) for n = 1..447</a>
%F A356010 E.g.f.: (1/(1-x)) * Sum_{k>0} x^k/(k * (1 - x^k)).
%F A356010 E.g.f.: -(1/(1-x)) * Sum_{k>0} log(1 - x^k).
%F A356010 a(n) ~ c * n! * n, where c = Pi^2/6. - _Vaclav Kotesovec_, Aug 02 2022
%F A356010 a(n) = n! * Sum_{k=1..n} sigma(k)/k. - _Seiichi Manyama_, Aug 03 2022
%p A356010 S:= ListTools:-PartialSums([seq(numtheory:-sigma(k)/k, k=1..30)]):
%p A356010 seq(n! * S[n], n=1..30); # _Robert Israel_, Aug 10 2025
%o A356010 (PARI) a(n) = n!*sum(k=1, n, n\k/k);
%o A356010 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, x^k/(k*(1-x^k)))/(1-x)))
%o A356010 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-x^k))/(1-x)))
%o A356010 (PARI) a(n) = n!*sum(k=1, n, sigma(k)/k); \\ _Seiichi Manyama_, Aug 03 2022
%Y A356010 Cf. A038048, A355886.
%K A356010 nonn
%O A356010 1,2
%A A356010 _Seiichi Manyama_, Jul 23 2022