%I #23 Aug 25 2024 18:57:38
%S 1,1,1,2,1,1,1,1,3,1,1,2,1,1,1,4,1,3,1,2,1,1,1,1,5,1,9,2,1,1,1,4,1,1,
%T 1,3,1,1,1,1,1,1,1,2,3,1,1,4,14,5,1,2,1,9,1,1,1,1,1,2,1,1,3,8,1,1,1,2,
%U 1,1,1,1,1,1,5,1,1,1,1,4,27,1,1,2,1,1,1,1,1,3,1,2,1,1,1,4,1,14,3,5,1,1,1,1
%N a(n) = denominator(A006571(n)/A366450(n)) if A366450(n) != 0, otherwise 1.
%C a(n) differs from A071974 at n = 27, 32, 36, 49, 54, 72, 76, 81, 96, 98, 100, 108, 116, 125, 135, 144,...
%C a(n) differs from A056622 at n = 27, 32, 36, 49, 54, 72, 76, 81, 96, 98, 100, 108, 116, 125, 128, 135, 144,...
%C GCD(a(n), A071974(n)) differs from A071974 at n = 36, 72, 76, 100, 116, 144,...
%C GCD(a(n), A056622(n)) differs from A056622 at n = 36, 72, 76, 100, 116, 128, 144,...
%t nn = 104; a[n_] := DivisorSum[n, MoebiusMu[#] # &]; f = (x^3 - x^2 - y^2 - y); w[n_] := SeriesCoefficient[q*(Product[(1 - q^k), {k, 11, n, 11}]*Product[1 - q^k, {k, n}])^2, {q, 0, n}]; A006571 = ParallelTable[w[n], {n, 1, nn}]; A366450 = ParallelTable[Sum[Sum[Sum[If[GCD[f, n] == k, 1, 0]*a[k]/n, {x, 1, n}], {y, 1, n}], {k, 1, n}], {n, 1, nn}]; Denominator[A006571/A366450]
%Y Cf. A006571, A366450, A056622, A071974.
%K nonn,frac
%O 1,4
%A _Mats Granvik_, Aug 19 2024