A372832 a(n) is the numerator of Sum_{d|n, d <= sqrt(n)} 1/d.
1, 1, 1, 3, 1, 3, 1, 3, 4, 3, 1, 11, 1, 3, 4, 7, 1, 11, 1, 7, 4, 3, 1, 25, 6, 3, 4, 7, 1, 61, 1, 7, 4, 3, 6, 9, 1, 3, 4, 39, 1, 2, 1, 7, 23, 3, 1, 9, 8, 17, 4, 7, 1, 2, 6, 53, 4, 3, 1, 49, 1, 3, 31, 15, 6, 2, 1, 7, 4, 129, 1, 19, 1, 3, 23, 7, 8, 2, 1, 83
Offset: 1
Examples
1, 1, 1, 3/2, 1, 3/2, 1, 3/2, 4/3, 3/2, 1, 11/6, 1, 3/2, 4/3, 7/4, 1, 11/6, ...
Links
- Antti Karttunen, Table of n, a(n) for n = 1..20000
Programs
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Mathematica
nmax = 80; CoefficientList[Series[Sum[x^(k^2)/(k (1 - x^k)), {k, 1, nmax}], {x, 0, nmax}], x] // Numerator // Rest -
PARI
a(n) = numerator(sumdiv(n, d, if (d^2 <= n, 1/d))); \\ Michel Marcus, May 14 2024
Formula
Numerators of coefficients in expansion of Sum_{k>=1} x^(k^2) / (k * (1 - x^k)).