On Near Perfect Numbers
Number Theory
2019-10-15 v4
Abstract
The study of perfect numbers (numbers which equal the sum of their proper divisors) goes back to antiquity, and is responsible for some of the oldest and most popular conjectures in number theory. We investigate a generalization introduced by Pollack and Shevelev: -near-perfect numbers. These are examples to the well-known pseudoperfect numbers first defined by Sierpi\'nski, and are numbers such that the sum of all but at most of its proper divisors equals the number. We establish their asymptotic order for all integers , as well as some properties of related quantities.
Keywords
Cite
@article{arxiv.1610.04253,
title = {On Near Perfect Numbers},
author = {Peter Cohen and Katherine Cordwell and Alyssa Epstein and Chung-Hang Kwan and Adam Lott and Steven J. Miller},
journal= {arXiv preprint arXiv:1610.04253},
year = {2019}
}
Comments
To appear in Acta Arithmetica (32 pages)