A366562 a(n) = Sum_{k=1..n} A366561(n,k)*A023900(k)/n.

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, -18, 0, -28, 0, -30, 0, 20, 0, 24, 0, -36, 0, 24, 0, -40, 0, -42, 0, 24, 0, -46, 0, -42, 0, 32, 0, -52, 0, 40, 0, 36, 0, -58, 0, -60, 0, 36, 0, 48, 0, -66, 0, 44, 0, -70, 0, -72, 0

Offset: 1

Author

Mats Granvik, Oct 13 2023

Keywords

• sign

Crossrefs

Cf. A000010, A001221, A366561, A366563.

Cf. A000265, A076479, A008683.

Programs

Mathematica

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}]

Formula

a(n) = Sum_{k=1..n} A366561(n,k)*A023900(k)/n.

Conjecture: a(n) = [Mod[n, 2] = 1]*A000010(n)*(-1)^A001221(n).

Conjectures from Ridouane Oudra, Jun 17 2025: (Start)

a(n) = (-1)^omega(n)*(2*phi(n) - phi(2*n)), where omega = A001221.

a(n) = (-1)^omega(n)*Sum_{d|n} mu(n/d)*A000265(d).

a(2*n) = 0.

a(2*n+1) = A076479(2*n+1)*phi(2*n+1). (End)