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A364047 Expansion of Sum_{k>0} x^k / (1 + x^(6*k)).

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%I A364047 #11 Jul 03 2023 11:47:03
%S A364047 1,1,1,1,1,1,0,1,1,1,1,1,2,0,1,1,1,1,0,1,0,1,1,1,2,2,1,0,1,1,0,1,1,1,
%T A364047 0,1,2,0,2,1,1,0,0,1,1,1,1,1,1,2,1,2,1,1,0,0,0,1,1,1,2,0,0,1,2,1,0,1,
%U A364047 1,0,1,1,2,2,2,0,0,2,0,1,1,1,1,0,2,0,1,1,1,1,0,1,0,1,0,1,2,1,1,2,1,1,0,2
%N A364047 Expansion of Sum_{k>0} x^k / (1 + x^(6*k)).
%F A364047 G.f.: Sum_{k>0} (-1)^(k-1) * x^(6*k-5) / (1 - x^(6*k-5)).
%F A364047 a(n) = Sum_{d|n, d==1 (mod 6)} (-1)^((d-1)/6).
%t A364047 a[n_] := DivisorSum[n, (-1)^((#-1)/6) &, Mod[#, 6] == 1 &]; Array[a, 100] (* _Amiram Eldar_, Jul 03 2023 *)
%o A364047 (PARI) a(n) = sumdiv(n, d, (d%6==1)*(-1)^((d-1)/6));
%Y A364047 Cf. A002654, A363037, A364011, A364043.
%Y A364047 Cf. A279060.
%K A364047 nonn
%O A364047 1,13
%A A364047 _Seiichi Manyama_, Jul 03 2023