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 A384817 #7 Jun 16 2025 18:52:58
%S A384817 1,2,3,17,21,25,29,17,173,191,209,463,499,535,571,2473,2617,2777,2921,
%T A384817 3101,3245,3389,3533,3713,96569,100169,34723,36223,37423,38623,39823,
%U A384817 20699,21299,21899,22499,69997,71797,73597,75397,77647,79447,81247,83047,85297
%N A384817 Numerator of the sum of the reciprocals of all square divisors of all positive integers <= n.
%F A384817 G.f. for fractions: (1/(1 - x)) * Sum_{k>=1} x^(k^2) / (k^2*(1 - x^(k^2))).
%F A384817 a(n) is the numerator of Sum_{k=1..floor(sqrt(n))} floor(n/k^2) / k^2.
%F A384817 a(n) / A384818(n) ~ Pi^4 * n / 90.
%e A384817 1, 2, 3, 17/4, 21/4, 25/4, 29/4, 17/2, 173/18, 191/18, 209/18, 463/36, ...
%t A384817 nmax = 44; CoefficientList[Series[1/(1 - x) Sum[x^(k^2)/(k^2 (1 - x^(k^2))), {k, 1, nmax}], {x, 0, nmax}], x] // Numerator // Rest
%t A384817 Table[Sum[Floor[n/k^2]/k^2, {k, 1, Floor[Sqrt[n]]}], {n, 1, 44}] // Numerator
%o A384817 (PARI) a(n) = numerator(sum(k=1, n, sumdiv(k, d, if (issquare(d), 1/d)))); \\ _Michel Marcus_, Jun 10 2025
%Y A384817 Cf. A007406, A017667, A284648, A309125, A373439, A384818 (denominators).
%K A384817 nonn,frac
%O A384817 1,2
%A A384817 _Ilya Gutkovskiy_, Jun 10 2025