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 A373582 #6 Jun 12 2024 17:36:04
%S A373582 1,0,-117,0,-350,0,-4263,0,-7533,0,-27225,0,-17914,0,62100,0,-53176,0,
%T A373582 -250173,0,83790,0,-541167,0,-168750,0,-557685,0,-459186,0,-1801875,0,
%U A373582 533610,0,2249100,0,-1223886,0,3157596,0,-1849100,0,-6717417,0,3863700,0,-9602523
%N A373582 a(n) = Sum_{k=1..n} Sum_{z=1..n} Sum_{y=1..n} Sum_{x=1..n} [GCD(f(x,y,z), n) = k] * f(x,y,z) * A023900(k), where f(x,y,z) = x^2 + y^2 - z^2.
%C A373582 Sign(a(n)) appears to be equal to A318657(n).
%C A373582 For n > 1, mod(a(n),2) appears to be equal to A354033(n).
%F A373582 a(n) = Sum_{k=1..n} Sum_{z=1..n} Sum_{y=1..n} Sum_{x=1..n} [GCD(f(x,y,z), n) = k] * f(x,y,z) * A023900(k), where f(x,y,z) = x^2 + y^2 - z^2.
%t A373582 nn = 47; a[n_] = DivisorSum[n, MoebiusMu[#] # &]; p = 2; f = x^p + y^p - z^p; ParallelTable[Sum[Sum[Sum[Sum[If[GCD[f, n] == k, f, 0] a[k], {x, 1, n}], {y, 1, n}], {z, 1, n}], {k, 1, n}], {n, 1, nn}]
%Y A373582 Cf. A368197, A023900, A318657, A354033.
%K A373582 sign
%O A373582 1,3
%A A373582 _Mats Granvik_, Jun 10 2024