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 A347176 #19 Mar 01 2023 02:02:16
%S A347176 1,1,1,-1,1,1,1,-1,4,1,1,-1,1,1,1,-5,1,4,1,-1,1,1,1,-1,6,1,4,-1,1,1,1,
%T A347176 -5,1,1,1,-4,1,1,1,-1,1,1,1,-1,4,1,1,-5,8,6,1,-1,1,4,1,-1,1,1,1,-1,1,
%U A347176 1,4,-13,1,1,1,-1,1,1,1,-4,1,1,6,-1,1,1,1,-5,13,1,1,-1,1,1,1,-1,1,4
%N A347176 G.f.: Sum_{k>=1} (-1)^(k+1) * k * x^(k^2) / (1 - x^(k^2)).
%C A347176 Excess of sum of square roots of odd square divisors of n over sum of square roots of even square divisors of n.
%H A347176 Amiram Eldar, <a href="/A347176/b347176.txt">Table of n, a(n) for n = 1..10000</a>
%F A347176 Multiplicative with a(2^e) = 3 - 2^(floor(e/2) + 1), and a(p^e) = (p^(floor(e/2) + 1) - 1)/(p - 1) for p > 2. - _Amiram Eldar_, Nov 15 2022
%F A347176 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log(2) (A002162). - _Amiram Eldar_, Mar 01 2023
%t A347176 nmax = 90; CoefficientList[Series[Sum[(-1)^(k + 1) k x^(k^2)/(1 - x^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A347176 Table[DivisorSum[n, (-1)^(# + 1) #^(1/2) &, IntegerQ[#^(1/2)] &], {n, 1, 90}]
%t A347176 f[p_, e_] := (p^(Floor[e/2] + 1) - 1)/(p - 1); f[2, e_] := 3 - 2^(Floor[e/2] + 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Nov 15 2022 *)
%o A347176 (PARI) a(n) = sumdiv(n, d, if (issquare(d), (-1)^((d%2)+1)*sqrtint(d))); \\ _Michel Marcus_, Aug 22 2021
%o A347176 (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i,1]==2, 3 - 2^(floor(f[i,2]/2) + 1), (f[i,1]^(floor(f[i,2]/2) + 1) - 1)/(f[i,1] - 1)));} \\ _Amiram Eldar_, Nov 15 2022
%Y A347176 Cf. A002129, A002162, A037213, A069290, A344299, A344300.
%K A347176 sign,mult
%O A347176 1,9
%A A347176 _Ilya Gutkovskiy_, Aug 21 2021