A372833 a(n) is the denominator of Sum_{d|n, d <= sqrt(n)} 1/d.

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

Offset: 1

Author

Ilya Gutkovskiy, May 14 2024

Keywords

• nonn
• frac

Comments

a(n) is a divisor of A072504(n). The first few values of n for which a(n) != A072504(n) are 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 110, ... . - Pontus von Brömssen, May 15 2024

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

Crossrefs

Cf. A017666, A066839, A072504, A372832 (numerators).

Programs

Mathematica

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

PARI

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

Formula

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