login
Expansion of Sum_{k>0} x^(5*k) / (1 + x^(6*k)).
0

%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