A364085 Expansion of Sum_{k>0} k * x^k / (1 - x^(4*k-1)).
1, 2, 3, 5, 5, 6, 8, 8, 11, 11, 11, 12, 14, 17, 15, 19, 17, 18, 24, 20, 21, 23, 25, 29, 29, 26, 27, 29, 35, 32, 32, 32, 33, 46, 35, 39, 40, 38, 47, 41, 41, 42, 49, 55, 45, 47, 50, 48, 64, 50, 53, 59, 53, 65, 56, 56, 57, 64, 71, 60, 69, 67, 63, 82, 67, 66, 68, 68, 86, 79, 71, 74, 74, 89, 81, 77, 77, 78
Offset: 1
Keywords
Programs
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Mathematica
a[n_] := DivisorSum[4*n - 1, # + 1 &, Mod[#, 4] == 3 &]/4; Array[a, 100] (* Amiram Eldar, Jul 05 2023 *)
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PARI
a(n) = sumdiv(4*n-1, d, (d%4==3)*(d+1))/4;
Formula
a(n) = (1/4) * Sum_{d | 4*n-1, d==3 (mod 4)} (d+1).
G.f.: Sum_{k>0} x^(3*k-2) / (1 - x^(4*k-3))^2.