A364063 Expansion of Sum_{k>0} k * x^k / (1 - x^(2*k-1)).
1, 3, 4, 5, 8, 7, 8, 14, 10, 11, 18, 13, 17, 22, 16, 17, 26, 26, 20, 30, 22, 23, 42, 25, 30, 38, 28, 38, 42, 31, 32, 55, 44, 35, 50, 37, 38, 65, 50, 41, 63, 43, 56, 62, 46, 58, 66, 62, 50, 81, 52, 53, 100, 55, 56, 78, 58, 74, 94, 74, 68, 86, 80, 65, 90, 67, 82, 124, 70, 71, 98, 86, 92, 117, 76, 77
Offset: 1
Keywords
Links
- Antti Karttunen, Table of n, a(n) for n = 1..20000
Programs
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Mathematica
a[n_] := DivisorSum[2*n - 1, # + 1 &]/2; Array[a, 100] (* Amiram Eldar, Jul 04 2023*)
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PARI
a(n) = sumdiv(2*n-1, d, d+1)/2;
Formula
a(n) = (1/2) * Sum_{d | 2*n-1} (d+1) = A007503(2*n-1)/2.
G.f.: Sum_{k>0} x^k / (1 - x^(2*k-1))^2.