A158274 Numerators of antiharmonic means of divisors of n.

1, 5, 5, 3, 13, 25, 25, 17, 7, 65, 61, 15, 85, 125, 65, 11, 145, 35, 181, 13, 125, 305, 265, 85, 21, 425, 41, 75, 421, 325, 481, 65, 305, 725, 325, 21, 685, 181, 425, 221, 841, 625, 925, 61, 91, 1325, 1105, 55, 43, 35

Offset

1,2

Comments

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

Links

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

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)).

Sum_{k=1..n} a(k)/A158275(k) ~ c * n^2, where c = (Pi^4/72) * Product_{p prime} (1 - (3*p-2)/(p^3)) = A152649 * A065473 = 0.387941... . - Amiram Eldar, Nov 21 2022

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000203, A001157, A020487, A065473, A152649, A158275 (denominators)

Sequence in context: A225666 A365078 A175505 * A202695 A110986 A193721

Adjacent sequences: A158271 A158272 A158273 * A158275 A158276 A158277

Keyword

nonn,frac

Author

Jaroslav Krizek, Mar 15 2009

Status

approved