A364044 - OEIS

%I #11 Jul 03 2023 11:45:04

%S 0,1,0,1,0,1,-1,1,0,1,0,2,0,0,0,1,-1,1,0,1,-1,2,0,2,0,1,-1,0,0,1,0,2,

%T 0,0,-1,2,-1,1,0,1,0,1,0,2,0,1,-1,2,-1,1,-1,2,0,0,0,0,-1,1,0,2,0,2,-1,

%U 2,0,2,-1,0,0,0,0,3,0,0,0,1,-2,1,0,1,-1,2,0,2,-1,1,-1,2,0,1,-1,2,0,0,0,3,-1,0,0,1

%N Expansion of Sum_{k>0} x^(2*k) / (1 + x^(5*k)).

%F G.f.: Sum_{k>0} (-1)^(k-1) * x^(5*k-3) / (1 - x^(5*k-3)).

%F a(n) = Sum_{d|n, d==2 (mod 5)} (-1)^d.

%t a[n_] := DivisorSum[n, (-1)^# &, Mod[#, 5] == 2 &]; Array[a, 100] (* _Amiram Eldar_, Jul 03 2023 *)

%o (PARI) a(n) = sumdiv(n, d, (d%5==2)*(-1)^d);

%Y Cf. A364043, A364045, A364046.

%Y Cf. A001877, A364020.

%K sign

%O 1,12

%A _Seiichi Manyama_, Jul 03 2023