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A326399 Expansion of Sum_{k>=1} k * x^k / (1 - x^(3*k)).

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%I A326399 #15 Jun 29 2023 13:22:07
%S A326399 1,2,3,5,5,6,8,10,9,11,11,15,14,16,15,21,17,18,20,27,24,23,23,30,26,
%T A326399 28,27,40,29,33,32,42,33,35,40,45,38,40,42,55,41,48,44,57,45,47,47,63,
%U A326399 57,57,51,70,53,54,56,80,60,59,59,81,62,64,72,85,70,69,68,87,69,88
%N A326399 Expansion of Sum_{k>=1} k * x^k / (1 - x^(3*k)).
%H A326399 Seiichi Manyama, <a href="/A326399/b326399.txt">Table of n, a(n) for n = 1..10000</a>
%F A326399 a(n) = Sum_{d|n, n/d==1 (mod 3)} d.
%F A326399 G.f.: Sum_{k>0} x^(3*k-2) / (1 - x^(3*k-2))^2. - _Seiichi Manyama_, Jun 29 2023
%t A326399 nmax = 70; CoefficientList[Series[Sum[k x^k/(1 - x^(3 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A326399 Table[DivisorSum[n, # &, MemberQ[{1}, Mod[n/#, 3]] &], {n, 1, 70}]
%Y A326399 Cf. A001817, A002131, A016777, A050460, A078181, A078708, A326400, A326401.
%K A326399 nonn
%O A326399 1,2
%A A326399 _Ilya Gutkovskiy_, Sep 11 2019