A364106 Expansion of Sum_{k>0} k * x^(3*k) / (1 - x^(5*k-1)).
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, 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, 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
Offset: 1
Keywords
Programs
-
Mathematica
a[n_] := DivisorSum[5*n - 3, # + 1 &, Mod[#, 5] == 4 &]/5; Array[a, 100] (* Amiram Eldar, Jul 12 2023 *)
-
PARI
a(n) = sumdiv(5*n-3, d, (d%5==4)*(d+1))/5;
Formula
a(n) = (1/5) * Sum_{d | 5*n-3, d==4 (mod 5)} (d+1).
G.f.: Sum_{k>0} x^(4*k-1) / (1 - x^(5*k-2))^2.