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A363901 Expansion of Sum_{k>0} x^k / (1 - x^(3*k))^2.

%I A363901 #18 Jun 29 2023 08:58:14
%S A363901 1,1,1,3,1,1,4,3,1,5,1,3,6,4,1,9,1,1,8,7,4,9,1,3,10,6,1,16,1,5,12,9,1,
%T A363901 13,4,3,14,8,6,21,1,4,16,11,1,17,1,9,21,14,1,26,1,1,20,16,8,21,1,7,22,
%U A363901 12,4,31,6,9,24,15,1,32,1,3,26,14,10,36,4,6,28,27,1,29,1,16,30,16,1,41,1
%N A363901 Expansion of Sum_{k>0} x^k / (1 - x^(3*k))^2.
%H A363901 Seiichi Manyama, <a href="/A363901/b363901.txt">Table of n, a(n) for n = 1..10000</a>
%F A363901 a(n) = (1/3) * Sum_{d|n, d==1 mod 3} (d+2) = (2 * A001817(n) + A078181(n))/3.
%F A363901 G.f.: Sum_{k>0} k * x^(3*k-2) / (1 - x^(3*k-2)).
%t A363901 a[n_] := DivisorSum[n, # + 2 &, Mod[#, 3] == 1 &]/3; Array[a, 100] (* _Amiram Eldar_, Jun 27 2023 *)
%o A363901 (PARI) a(n) = sumdiv(n, d, (d%3==1)*(d+2))/3;
%Y A363901 Cf. A001817, A078181.
%Y A363901 Cf. A113415, A363903.
%K A363901 nonn
%O A363901 1,4
%A A363901 _Seiichi Manyama_, Jun 27 2023