A364933 a(n) = Sum_{k=1..n} A191898(n,k)*[A191904(n,k) = A191898(n,k)].

0, -1, -1, 0, -1, -2, -1, 2, 3, -2, -1, 0, -1, -2, 1, 6, -1, 2, -1, 2, 3, -2, -1, 4, 15, -2, 15, 4, -1, 0, -1, 14, 7, -2, 13, 8, -1, -2, 9, 10, -1, 2, -1, 8, 17, -2, -1, 12, 35, 14, 13, 10, -1, 14, 25, 16, 15, -2, -1, 8, -1, -2, 27, 30, 31, 6, -1, 14, 19, 12

Offset: 1

Author

Mats Granvik, Aug 13 2023

Keywords

• sign

Crossrefs

Cf. A191898, A191904, A057859, A008472.

Programs

Mathematica

f[n_] := DivisorSum[n, MoebiusMu[#] # &]; Table[Sum[If[If[Mod[n, k] == 0, 1 - k, 1] == f[GCD[n, k]], f[GCD[n, k]], 0], {k, 1, n}], {n, 1, 70}]

Formula

a(n) = Sum_{k=1..n} A191898(n,k)*[A191904(n,k) = A191898(n,k)].

Conjecture: a(n) = A057859(n) - A008472(n) - 1.