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

1,4

Links

Table of n, a(n) for n=1..80.

Formula

Numerators of coefficients in expansion of Sum_{k>=1} x^(k^2) / (k * (1 - x^k)).

Example

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, ...

Mathematica

nmax = 80; CoefficientList[Series[Sum[x^(k^2)/(k (1 - x^k)), {k, 1, nmax}], {x, 0, nmax}], x] // Numerator // Rest

Prog

(PARI) a(n) = numerator(sumdiv(n, d, if (d^2 <= n, 1/d))); \\ Michel Marcus, May 14 2024

Crossrefs

Cf. A017665, A066839, A372833 (denominators).

Sequence in context: A109599 A333752 A066839 * A176246 A046933 A185091

Adjacent sequences: A372829 A372830 A372831 * A372833 A372834 A372835

Keyword

nonn,frac

Author

Ilya Gutkovskiy, May 14 2024

Status

approved