A363902 - OEIS

%I #22 Jun 29 2023 08:58:11

%S 0,1,0,1,2,1,0,4,0,3,4,1,0,6,2,4,6,1,0,10,0,5,8,4,2,10,0,6,10,3,0,15,

%T 4,7,14,1,0,14,0,13,14,6,0,20,2,9,16,4,0,20,6,10,18,1,6,28,0,11,20,10,

%U 0,22,0,15,24,5,0,30,8,20,24,4,0,26,2,14,30,10,0,40,0,15,28,6,8

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

%H Seiichi Manyama, <a href="/A363902/b363902.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (1/3) * Sum_{d|n, d==2 mod 3} (d+1) = (A001822(n) + A078182(n))/3.

%F G.f.: Sum_{k>0} k * x^(3*k-1) / (1 - x^(3*k-1)).

%t a[n_] := DivisorSum[n, # + 1 &, Mod[#, 3] == 2 &]/3; Array[a, 100] (* _Amiram Eldar_, Jun 27 2023 *)

%o (PARI) a(n) = sumdiv(n, d, (d%3==2)*(d+1))/3;

%Y Cf. A001822, A078182, A363901.

%Y Cf. A113415, A363904.

%K nonn

%O 1,5

%A _Seiichi Manyama_, Jun 27 2023