On the Within-perfect Numbers

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...

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Bibliographic Details
Published in:arXiv.org 2024-09
Main Authors: Chung-Hang, Kwan, Miller, Steven J
Format: Article
Language:English
Subjects:
Number theory
Real numbers
Online Access:Get full text
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Summary: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.
ISSN:2331-8422