A364105 Expansion of Sum_{k>0} k * x^(2*k) / (1 - x^(5*k-1)).
0, 1, 0, 2, 0, 4, 0, 4, 0, 6, 0, 6, 2, 8, 0, 8, 0, 10, 0, 13, 0, 14, 0, 12, 0, 14, 4, 14, 0, 16, 2, 16, 0, 26, 0, 18, 0, 20, 0, 22, 6, 22, 0, 22, 0, 28, 0, 34, 2, 26, 0, 26, 0, 28, 8, 28, 0, 37, 0, 30, 0, 44, 0, 32, 4, 34, 2, 34, 10, 42, 0, 36, 0, 38, 0, 54, 0, 40, 0, 40, 0, 54, 12, 46, 2, 44, 0, 44, 0
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[5*n - 2, # + 1 &, Mod[#, 5] == 4 &]/5; Array[a, 100] (* Amiram Eldar, Jul 12 2023 *)
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PARI
a(n) = sumdiv(5*n-2, d, (d%5==4)*(d+1))/5;
Formula
a(n) = (1/5) * Sum_{d | 5*n-2, d==4 (mod 5)} (d+1).
G.f.: Sum_{k>0} x^(4*k-2) / (1 - x^(5*k-3))^2.