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 A384818 #7 Jun 16 2025 18:53:04
%S A384818 1,1,1,4,4,4,4,2,18,18,18,36,36,36,36,144,144,144,144,144,144,144,144,
%T A384818 144,3600,3600,1200,1200,1200,1200,1200,600,600,600,600,1800,1800,
%U A384818 1800,1800,1800,1800,1800,1800,1800,600,600,600,1200,58800,58800,58800,58800,58800
%N A384818 Denominator of the sum of the reciprocals of all square divisors of all positive integers <= n.
%F A384818 G.f. for fractions: (1/(1 - x)) * Sum_{k>=1} x^(k^2) / (k^2*(1 - x^(k^2))).
%F A384818 a(n) is the denominator of Sum_{k=1..floor(sqrt(n))} floor(n/k^2) / k^2.
%F A384818 A384817(n) / a(n) ~ Pi^4 * n / 90.
%e A384818 1, 2, 3, 17/4, 21/4, 25/4, 29/4, 17/2, 173/18, 191/18, 209/18, 463/36, ...
%t A384818 nmax = 53; CoefficientList[Series[1/(1 - x) Sum[x^(k^2)/(k^2 (1 - x^(k^2))), {k, 1, nmax}], {x, 0, nmax}], x] // Denominator // Rest
%t A384818 Table[Sum[Floor[n/k^2]/k^2, {k, 1, Floor[Sqrt[n]]}], {n, 1, 53}] // Denominator
%o A384818 (PARI) a(n) = denominator(sum(k=1, n, sumdiv(k, d, if (issquare(d), 1/d)))); \\ _Michel Marcus_, Jun 10 2025
%Y A384818 Cf. A007407, A017668, A284650, A309125, A373440, A384817 (numerators).
%K A384818 nonn,frac
%O A384818 1,4
%A A384818 _Ilya Gutkovskiy_, Jun 10 2025