Year: 2009
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Bosma, Wieb, Kane, Ben
Institution: Radboud University Nijmegen
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949469299