On the Within-perfect Numbers

Chung-Hang Kwan; Steven J. Miller

On the Within-perfect Numbers

Number Theory 2024-09-11 v2

Authors: Chung-Hang Kwan , Steven J. Miller

Abstract

Motivated by the works of Erd\"os, Pomerance, Wolke and Harman on the sum-of-divisor function $\sigma(n)$ , we study the distribution of a special class of natural numbers closely related to (multiply) perfect numbers which we term ` $(\ell;k)$ -within-perfect numbers', where $\ell >1$ is a real number and $k: [1, \infty) \rightarrow (0, \infty)$ is an increasing and unbounded function.

Keywords

divisor function perfect numbers

Cite

@article{arxiv.2406.06892,
  title  = {On the Within-perfect Numbers},
  author = {Chung-Hang Kwan and Steven J. Miller},
  journal= {arXiv preprint arXiv:2406.06892},
  year   = {2024}
}

Comments

Minor changes, Accepted for publication. This article together with arXiv:1610.04253v4 (published in Acta Arithmetica 194 (2020), 341-366) supersede arXiv:1610.04253v2

On the Within-perfect Numbers

Abstract

Keywords

Cite

Comments

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