A364107 - OEIS

%I #13 Jul 12 2023 01:01:21

%S 0,0,0,1,0,0,0,3,0,0,0,4,0,0,0,5,2,0,0,6,0,0,0,7,0,5,0,8,0,0,0,9,0,0,

%T 6,10,0,0,0,14,0,0,0,19,0,0,0,13,0,0,0,14,8,7,0,15,0,0,0,16,0,9,0,17,

%U 0,0,0,26,0,0,10,19,4,0,0,20,0,0,0,32,0,9,0,22,0,0,0,23,12,0,0,33,0,0,0

%N Expansion of Sum_{k>0} k * x^(4*k) / (1 - x^(5*k-1)).

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

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

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

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

%Y Cf. A364104, A364105, A364106.

%Y Cf. A359241, A364103.

%K nonn

%O 1,8

%A _Seiichi Manyama_, Jul 05 2023