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A364012 Expansion of Sum_{k>0} k * x^k / (1 + x^(3*k)).

%I A364012 #21 Jul 02 2023 10:03:09
%S A364012 1,2,3,3,5,6,8,6,9,9,11,9,14,16,15,11,17,18,20,13,24,21,23,18,26,28,
%T A364012 27,24,29,27,32,22,33,33,40,27,38,40,42,25,41,48,44,31,45,45,47,33,57,
%U A364012 47,51,42,53,54,56,48,60,57,59,39,62,64,72,43,70,63,68,49,69,72,71,54,74,76,78
%N A364012 Expansion of Sum_{k>0} k * x^k / (1 + x^(3*k)).
%H A364012 Seiichi Manyama, <a href="/A364012/b364012.txt">Table of n, a(n) for n = 1..10000</a>
%F A364012 G.f.: Sum_{k>0} (-1)^(k-1) * x^(3*k-2) / (1 - x^(3*k-2))^2.
%F A364012 a(n) = -Sum_{d|n, n/d==1 (mod 3)} (-1)^(n/d) * d.
%t A364012 a[n_] := -DivisorSum[n, (-1)^(n/#) * # &, Mod[n/#, 3] == 1 &]; Array[a, 100] (* _Amiram Eldar_, Jul 01 2023 *)
%o A364012 (PARI) a(n) = -sumdiv(n, d, (n/d%3==1)*(-1)^(n/d)*d);
%Y A364012 Cf. A364011, A364013.
%Y A364012 Cf. A050469, A364019, A364031.
%K A364012 nonn
%O A364012 1,2
%A A364012 _Seiichi Manyama_, Jul 01 2023