This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A364065 #21 Jul 06 2023 08:55:27 %S A364065 1,1,3,1,4,1,7,1,6,1,9,4,8,1,11,1,14,1,16,1,12,6,15,1,14,4,27,1,16,1, %T A364065 19,8,21,1,26,1,32,1,23,4,22,10,31,1,24,1,44,6,26,1,36,12,28,4,31,1, %U A364065 46,1,47,1,40,14,35,1,34,1,64,4,36,8,39,16,38,6,60,1,60,1,43,1,50,21,56,1,44,1,74,1,56,1 %N A364065 Expansion of Sum_{k>0} k * x^(2*k-1) / (1 - x^(3*k-2)). %H A364065 Seiichi Manyama, <a href="/A364065/b364065.txt">Table of n, a(n) for n = 1..10000</a> %F A364065 a(n) = (1/3) * Sum_{d | 3*n-1, d==1 (mod 3)} (d+2). %F A364065 G.f.: Sum_{k>0} x^k / (1 - x^(3*k-1))^2. %t A364065 a[n_] := DivisorSum[3*n - 1, # + 2 &, Mod[#, 3] == 1 &]/3; Array[a, 100] (* _Amiram Eldar_, Jul 05 2023 *) %o A364065 (PARI) a(n) = sumdiv(3*n-1, d, (d%3==1)*(d+2))/3; %Y A364065 Cf. A359211, A363514. %K A364065 nonn %O A364065 1,3 %A A364065 _Seiichi Manyama_, Jul 04 2023