A372835 a(n) is the denominator of Sum_{d|n, d < sqrt(n)} 1/d.

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 4, 3, 2, 1, 12, 1, 2, 3, 4, 1, 30, 1, 4, 3, 2, 5, 12, 1, 2, 3, 20, 1, 1, 1, 4, 15, 2, 1, 4, 1, 10, 3, 4, 1, 1, 5, 28, 3, 2, 1, 20, 1, 2, 21, 4, 5, 1, 1, 4, 3, 70, 1, 8, 1, 2, 15, 4, 7, 1, 1, 40

Offset

1,6

Links

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

Formula

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

Example

0, 1, 1, 1, 1, 3/2, 1, 3/2, 1, 3/2, 1, 11/6, 1, 3/2, 4/3, 3/2, 1, 11/6, ...

Mathematica

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

Prog

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

Crossrefs

Cf. A017666, A070039, A372834 (numerators).

Sequence in context: A322401 A124333 A144757 * A363520 A215136 A318658

Adjacent sequences: A372832 A372833 A372834 * A372836 A372837 A372838

Keyword

nonn,frac

Author

Ilya Gutkovskiy, May 14 2024

Status

approved