A364106 - OEIS

%I #13 Jul 12 2023 01:01:19

%S 0,0,1,0,0,2,1,0,3,0,1,4,0,0,8,0,0,6,1,0,7,0,4,10,0,0,10,0,0,10,5,0,

%T 13,0,1,12,3,0,19,0,0,16,1,0,15,0,7,16,0,4,23,0,0,18,8,0,19,0,1,22,0,

%U 0,35,0,3,22,1,0,29,0,10,24,0,0,26,6,0,28,14,0,27,0,1,28,0,0,48,4,7,30,1,0

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

%F a(n) = (1/5) * Sum_{d | 5*n-3, d==4 (mod 5)} (d+1).

%F G.f.: Sum_{k>0} x^(4*k-1) / (1 - x^(5*k-2))^2.

%t a[n_] := DivisorSum[5*n - 3, # + 1 &, Mod[#, 5] == 4 &]/5; Array[a, 100] (* _Amiram Eldar_, Jul 12 2023 *)

%o (PARI) a(n) = sumdiv(5*n-3, d, (d%5==4)*(d+1))/5;

%Y Cf. A364104, A364105, A364107.

%Y Cf. A359270, A364102.

%K nonn

%O 1,6

%A _Seiichi Manyama_, Jul 05 2023