A344369 Dirichlet g.f.: Product_{k>=2} 1 / (1 + k^(1-s)).

1, -2, -3, 0, -5, 0, -7, -8, 0, 0, -11, 0, -13, 0, 0, 16, -17, 0, -19, 0, 0, 0, -23, 24, 0, 0, -27, 0, -29, 30, -31, -32, 0, 0, 0, 36, -37, 0, 0, 40, -41, 42, -43, 0, 0, 0, -47, 0, 0, 0, 0, 0, -53, 54, 0, 56, 0, 0, -59, 60, -61, 0, 0, 64, 0, 66, -67, 0, 0, 70

Offset: 1

Author

Ilya Gutkovskiy, May 16 2021

Keywords

• sign

Crossrefs

Cf. A022693, A224892, A316441, A328731, A344368, A344370.

Programs

Mathematica

facs[n_] := If[n <= 1, {{}}, Join @@ Table[Map[Prepend[#, d] &, Select[facs[n/d], Min @@ # >= d &]], {d, Rest[Divisors[n]]}]]; A316441[n_] := Sum[(-1)^Length[f], {f, facs[n]}]; Table[n A316441[n], {n, 70}]

Formula

a(n) = n * A316441(n).