A344369 - OEIS

%I #5 May 16 2021 12:25:34

%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,

%T -27,0,-29,30,-31,-32,0,0,0,36,-37,0,0,40,-41,42,-43,0,0,0,-47,0,0,0,

%U 0,0,-53,54,0,56,0,0,-59,60,-61,0,0,64,0,66,-67,0,0,70

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

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

%t 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}]

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

%K sign

%O 1,2

%A _Ilya Gutkovskiy_, May 16 2021