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 A344300 #15 Nov 15 2022 09:17:28
%S A344300 1,1,1,-3,1,1,1,-3,10,1,1,-3,1,1,1,-19,1,10,1,-3,1,1,1,-3,26,1,10,-3,
%T A344300 1,1,1,-19,1,1,1,-30,1,1,1,-3,1,1,1,-3,10,1,1,-19,50,26,1,-3,1,10,1,
%U A344300 -3,1,1,1,-3,1,1,10,-83,1,1,1,-3,1,1,1,-30,1,1,26,-3,1,1,1,-19
%N A344300 Expansion of Sum_{k>=1} (-1)^(k+1) * k^2 * x^(k^2) / (1 - x^(k^2)).
%C A344300 Excess of sum of odd squares dividing n over sum of even squares dividing n.
%H A344300 Amiram Eldar, <a href="/A344300/b344300.txt">Table of n, a(n) for n = 1..10000</a>
%F A344300 Multiplicative with a(2^e) = 2 - (2^(2*floor(e/2) + 2) - 1)/3, and a(p^e) = (p^(2*floor(e/2) + 2) - 1)/(p^2 - 1) for p > 2. - _Amiram Eldar_, Nov 15 2022
%t A344300 nmax = 80; CoefficientList[Series[Sum[(-1)^(k + 1) k^2 x^(k^2)/(1 - x^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A344300 Table[DivisorSum[n, (-1)^(# + 1) # &, IntegerQ[#^(1/2)] &], {n, 1, 80}]
%t A344300 f[p_, e_] := (p^(2*Floor[e/2] + 2) - 1)/(p^2 - 1); f[2, e_] := 2 - (2^(2*Floor[e/2] + 2) - 1)/3; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Nov 15 2022 *)
%o A344300 (PARI) a(n) = sumdiv(n, d, if (issquare(d), (-1)^((d%2)+1)*d)); \\ _Michel Marcus_, Aug 22 2021
%o A344300 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i,1]==2, 2 - (2^(2*floor(f[i,2]/2) + 2) - 1)/3, (f[i,1]^(2*floor(f[i,2]/2) + 2) - 1)/(f[i,1]^2 - 1)));} \\ _Amiram Eldar_, Nov 15 2022
%Y A344300 Cf. A002129, A035316, A300853, A321543, A344299.
%K A344300 sign,mult
%O A344300 1,4
%A A344300 _Ilya Gutkovskiy_, May 14 2021