English

The aliquot constant

Number Theory 2009-12-21 v1

Abstract

The average value of log s(n)/n taken over the first N even integers is shown to converge to a constant lambda when N tends to infinity; moreover, the value of this constant is approximated and proven to be less than 0. Here s(n) sums the divisors of n less than n. Thus the geometric mean of s(n)/n, the growth factor of the function s, in the long run tends to be less than 1. This could be interpreted as probabilistic evidence that aliquot sequences tend to remain bounded.

Keywords

Cite

@article{arxiv.0912.3660,
  title  = {The aliquot constant},
  author = {Wieb Bosma and Ben Kane},
  journal= {arXiv preprint arXiv:0912.3660},
  year   = {2009}
}

Comments

16 pages

R2 v1 2026-06-21T14:25:40.251Z