A158275 Denominators of antiharmonic means of divisors of n.

1, 3, 2, 1, 3, 6, 4, 3, 1, 9, 6, 2, 7, 12, 6, 1, 9, 3, 10, 1, 8, 18, 12, 6, 1, 21, 2, 4, 15, 18, 16, 3, 12, 27, 12, 1, 19, 6, 14, 9, 21, 24, 22, 2, 3, 36, 24, 2, 1, 1

Offset: 1

Author

Jaroslav Krizek, Mar 15 2009

Keywords

• nonn
• frac

Comments

Numbers k such that sigma_2(k)/sigma_1(k) = A001157(k)/A000203(k) are integers are in A020487.

Examples

			Antiharmonic means of divisors of n>=1: 1, 5/3, 5/2, 3, 13/2, 25/6, ...
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001157, A000203, A020487, A158274 (numerators).

Programs

Mathematica

Table[Denominator[DivisorSigma[2, n]/DivisorSigma[1, n]], {n, 50}] (* Ivan Neretin, May 22 2015 *)

PARI

a(n) = denominator(sigma(n,2)/sigma(n)); \\ Amiram Eldar, Nov 21 2022

Formula

Antiharmonic mean of divisors of number n = Product (p_i^e_i) is sigma_2(n)/sigma_1(n) = A001157(n)/A000203(n) = Product ((p_i^(e_i+1)+1)/(p_i+1)).

a(A020487(n)) = 1. - Amiram Eldar, Nov 21 2022