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 A356297 #18 Aug 07 2022 04:50:19
%S A356297 1,4,16,82,458,3228,24036,212448,2032992,21781440,246853440,
%T A356297 3201742080,42580650240,621037186560,9664270963200,161166707251200,
%U A356297 2781679603046400,52204357423411200,1004687538456268800,20823621371578368000,447027656835852288000
%N A356297 a(n) = n! * Sum_{k=1..n} sigma_0(k)/k.
%F A356297 E.g.f.: -(1/(1-x)) * Sum_{k>0} log(1 - x^k)/k.
%F A356297 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
%t A356297 Table[n! * Sum[DivisorSigma[0, k]/k, {k, 1, n}], {n, 1, 20}] (* _Vaclav Kotesovec_, Aug 07 2022 *)
%o A356297 (PARI) a(n) = n!*sum(k=1, n, sigma(k, 0)/k);
%o A356297 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-x^k)/k)/(1-x)))
%Y A356297 Cf. A000005, A006218, A356010, A356298, A356323.
%K A356297 nonn
%O A356297 1,2
%A A356297 _Seiichi Manyama_, Aug 03 2022