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 A373439 #17 Jun 26 2024 06:01:58
%S A373439 1,1,1,5,1,1,1,5,10,1,1,5,1,1,1,21,1,10,1,5,1,1,1,5,26,1,10,5,1,1,1,
%T A373439 21,1,1,1,25,1,1,1,5,1,1,1,5,10,1,1,21,50,26,1,5,1,10,1,5,1,1,1,5,1,1,
%U A373439 10,85,1,1,1,5,1,1,1,25,1,1,26,5,1,1,1,21,91,1,1,5,1
%N A373439 Numerator of sum of reciprocals of square divisors of n.
%H A373439 Amiram Eldar, <a href="/A373439/b373439.txt">Table of n, a(n) for n = 1..10000</a>
%F A373439 Numerators of coefficients in expansion of Sum_{k>=1} x^(k^2)/(k^2*(1 - x^(k^2))).
%F A373439 a(n) is the numerator of Sum_{d^2|n} 1/d^2.
%F A373439 From _Amiram Eldar_, Jun 26 2024: (Start)
%F A373439 Let f(n) = a(n)/A373440(n). Then:
%F A373439 f(n) is multiplicative with f(p^e) = (p^2 - p^(-2*floor(e/2)))/(p^2-1).
%F A373439 Dirichlet g.f. of f(n): zeta(s) * zeta(2*s+2).
%F A373439 Sum_{k=1..n} f(k) ~ zeta(4) * n. (End)
%e A373439 1, 1, 1, 5/4, 1, 1, 1, 5/4, 10/9, 1, 1, 5/4, 1, 1, 1, 21/16, 1, 10/9, 1, 5/4, 1, 1, 1, 5/4, 26/25, ...
%t A373439 nmax = 85; CoefficientList[Series[Sum[x^(k^2)/(k^2 (1 - x^(k^2))), {k, 1, nmax}], {x, 0, nmax}], x] // Rest // Numerator
%t A373439 f[p_, e_] := (p^2 - p^(-2*Floor[e/2]))/(p^2-1); a[1] = 1; a[n_] := Numerator[Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* _Amiram Eldar_, Jun 26 2024 *)
%o A373439 (PARI) a(n) = numerator(sumdiv(n, d, if (issquare(d), 1/d))); \\ _Michel Marcus_, Jun 05 2024
%Y A373439 Cf. A007406, A017665, A017667, A028235, A035316, A332880, A373440 (denominators).
%K A373439 nonn,frac
%O A373439 1,4
%A A373439 _Ilya Gutkovskiy_, Jun 05 2024