A363928 - OEIS

%I #14 Jun 30 2023 08:36:08

%S 0,0,1,0,0,1,0,2,1,0,0,1,3,0,1,2,0,5,0,0,1,0,5,3,0,3,1,6,0,1,0,2,8,0,

%T 0,5,0,8,4,2,0,1,9,0,1,5,0,13,0,0,1,3,11,5,0,8,1,12,0,1,0,0,14,2,3,8,

%U 0,14,6,0,0,7,15,0,1,8,0,20,0,2,1,0,17,7,0,9,1,20,0,5,3,5,20,0,0,13,0,20,8,0,0

%N Expansion of Sum_{k>0} x^(3*k) / (1 - x^(5*k))^2.

%H Seiichi Manyama, <a href="/A363928/b363928.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = (1/5) * Sum_{d|n, d==3 mod 5} (d+2) = (2 * A001878(n) + A284281(n))/5.

%F G.f.: Sum_{k>0} k * x^(5*k-2) / (1 - x^(5*k-2)).

%t a[n_] := DivisorSum[n, # + 2 &, Mod[#, 5] == 3 &] / 5; Array[a, 100] (* _Amiram Eldar_, Jun 28 2023 *)

%o (PARI) a(n) = sumdiv(n, d, (d%5==3)*(d+2))/5;

%Y Cf. A363925, A363926, A363929.

%Y Cf. A001878, A284281.

%K nonn

%O 1,8

%A _Seiichi Manyama_, Jun 28 2023