%I #11 Jul 03 2023 11:48:41
%S 0,0,0,0,1,0,0,0,0,1,-1,0,0,0,1,0,1,0,0,1,0,-1,-1,0,1,0,0,0,1,1,0,0,
%T -1,1,0,0,0,0,0,1,1,0,0,-1,1,-1,-1,0,0,1,1,0,1,0,0,0,0,1,-1,1,0,0,0,0,
%U 2,-1,0,1,-1,0,-1,0,0,0,1,0,0,0,0,1,0,1,-1,0,2,0,1,-1,1,1,0,-1,0,-1,0,0,0,0,-1,1,1,1
%N Expansion of Sum_{k>0} x^(5*k) / (1 + x^(6*k)).
%F G.f.: Sum_{k>0} (-1)^(k-1) * x^(6*k-1) / (1 - x^(6*k-1)).
%F a(n) = Sum_{d|n, d==5 (mod 6)} (-1)^((d-5)/6).
%t a[n_] := DivisorSum[n, (-1)^((#-5)/6) &, Mod[#, 6] == 5 &]; Array[a, 100] (* _Amiram Eldar_, Jul 03 2023 *)
%o (PARI) a(n) = sumdiv(n, d, (d%6==5)*(-1)^((d-5)/6));
%Y Cf. A319995.
%K sign
%O 1,65
%A _Seiichi Manyama_, Jul 03 2023