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A364066 Expansion of Sum_{k>0} k * x^k / (1 - x^(3*k-1)).

%I A364066 #23 Jul 06 2023 08:00:03
%S A364066 1,2,4,4,6,6,10,8,10,10,15,14,14,14,20,16,20,18,28,20,22,24,30,24,26,
%T A364066 30,40,28,30,30,40,34,39,34,48,36,44,38,50,46,42,44,58,44,46,46,74,52,
%U A364066 50,50,68,54,54,62,70,56,66,58,82,60,76,64,80,64,66,66,97,78,70,74,90,74,74,80,114,76,88,78,100
%N A364066 Expansion of Sum_{k>0} k * x^k / (1 - x^(3*k-1)).
%H A364066 Seiichi Manyama, <a href="/A364066/b364066.txt">Table of n, a(n) for n = 1..10000</a>
%F A364066 a(n) = (1/3) * Sum_{d | 3*n-1, d==2 (mod 3)} (d+1).
%F A364066 G.f.: Sum_{k>0} x^(2*k-1) / (1 - x^(3*k-2))^2.
%t A364066 a[n_] := DivisorSum[3*n - 1, # + 1 &, Mod[#, 3] == 2 &]/3; Array[a, 100] (* _Amiram Eldar_, Jul 05 2023 *)
%o A364066 (PARI) a(n) = sumdiv(3*n-1, d, (d%3==2)*(d+1))/3;
%Y A364066 Cf. A364063, A364085.
%Y A364066 Cf. A359211, A363890.
%K A364066 nonn
%O A364066 1,2
%A A364066 _Seiichi Manyama_, Jul 04 2023