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%I #10 Oct 14 2023 14:07:11
%S 1,0,-2,0,-4,0,-6,0,-6,0,-10,0,-12,0,8,0,-16,0,-18,0,12,0,-22,0,-20,0,
%T -18,0,-28,0,-30,0,20,0,24,0,-36,0,24,0,-40,0,-42,0,24,0,-46,0,-42,0,
%U 32,0,-52,0,40,0,36,0,-58,0,-60,0,36,0,48,0,-66,0,44,0,-70,0,-72,0
%N a(n) = Sum_{k=1..n} A366561(n,k)*A023900(k)/n.
%F a(n) = Sum_{k=1..n} A366561(n,k)*A023900(k)/n.
%F Conjecture: a(n) = [Mod[n, 2] = 1]*A000010(n)*(-1)^A001221(n).
%t nn = 74; f = x^2 - y^2; g[n_] := DivisorSum[n, MoebiusMu[#] # &]; Table[Sum[Sum[Sum[If[GCD[f, n] == k, 1, 0]*g[k]/n, {x, 1, n}], {y, 1, n}], {k, 1, n}], {n, 1, nn}]
%Y Cf. A000010, A001221, A366561, A366563.
%K sign
%O 1,3
%A _Mats Granvik_, Oct 13 2023