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 A344299 #14 Nov 15 2022 09:17:32
%S A344299 1,1,1,0,1,1,1,0,2,1,1,0,1,1,1,-1,1,2,1,0,1,1,1,0,2,1,2,0,1,1,1,-1,1,
%T A344299 1,1,0,1,1,1,0,1,1,1,0,2,1,1,-1,2,2,1,0,1,2,1,0,1,1,1,0,1,1,2,-2,1,1,
%U A344299 1,0,1,1,1,0,1,1,2,0,1,1,1,-1,3,1,1,0,1,1,1,0,1,2
%N A344299 Expansion of Sum_{k>=1} (-1)^(k+1) * x^(k^2) / (1 - x^(k^2)).
%C A344299 Number of odd squares dividing n minus number of even squares dividing n.
%C A344299 Inverse Moebius transform of A258998.
%H A344299 Amiram Eldar, <a href="/A344299/b344299.txt">Table of n, a(n) for n = 1..10000</a>
%F A344299 G.f.: Sum_{k>=1} (1 - theta_4(x^k)) / 2.
%F A344299 From _Amiram Eldar_, Nov 15 2022: (Start)
%F A344299 Multiplicative with a(2^e) = 1 - floor(e/2), and a(p^e) = 1 + floor(e/2) for p > 2.
%F A344299 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Pi^2/12 (A072691). (End)
%t A344299 nmax = 90; CoefficientList[Series[Sum[(-1)^(k + 1) x^(k^2)/(1 - x^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A344299 Table[DivisorSum[n, (-1)^(# + 1) &, IntegerQ[#^(1/2)] &], {n, 1, 90}]
%t A344299 f[p_, e_] := 1 - (-1)^p*Floor[e/2]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Nov 15 2022 *)
%o A344299 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, 1 - (-1)^f[i,1] * floor(f[i,2]/2));} \\ _Amiram Eldar_, Nov 15 2022
%Y A344299 Cf. A046951, A048272, A072691, A258998, A317529, A344300.
%K A344299 sign,mult
%O A344299 1,9
%A A344299 _Ilya Gutkovskiy_, May 14 2021