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A364043 Expansion of Sum_{k>0} x^k / (1 + x^(5*k)).

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%I A364043 #12 Jul 05 2023 01:45:10
%S A364043 1,1,1,1,1,0,1,1,1,1,2,0,1,1,1,0,1,0,1,1,2,2,1,0,1,0,1,1,1,0,2,0,2,1,
%T A364043 1,-1,1,1,1,1,2,1,1,2,1,0,1,-1,1,1,2,0,1,0,2,0,1,1,1,0,2,2,2,0,1,0,1,
%U A364043 1,1,1,2,-1,1,1,1,0,2,-1,1,0,2,2,1,1,1,0,1,2,1,0,2,0,2,1,1,-2,1,1,2,1,2,1,1
%N A364043 Expansion of Sum_{k>0} x^k / (1 + x^(5*k)).
%F A364043 G.f.: Sum_{k>0} (-1)^(k-1) * x^(5*k-4) / (1 - x^(5*k-4)).
%F A364043 a(n) = -Sum_{d|n, d==1 (mod 5)} (-1)^d.
%t A364043 a[n_] := -DivisorSum[n, (-1)^# &, Mod[#, 5] == 1 &]; Array[a, 100] (* _Amiram Eldar_, Jul 05 2023 *)
%o A364043 (PARI) a(n) = -sumdiv(n, d, (d%5==1)*(-1)^d);
%Y A364043 Cf. A364044, A364045, A364046.
%Y A364043 Cf. A002654, A363037, A364011, A364047.
%Y A364043 Cf. A001876, A364019.
%K A364043 sign
%O A364043 1,11
%A A364043 _Seiichi Manyama_, Jul 03 2023