On finiteness of odd superperfect numbers

Some new results concerning the equation \(\sigma(N)=aM, \sigma(M)=bN\) are proved. As a corollary, there are only finitely many odd superperfect numbers with a fixed number of distinct prime factors.

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Bibliographic Details
Published in	arXiv.org
Main Author	Yamada, Tomohiro
Format	Paper Journal Article
Language	English
Published	Ithaca Cornell University Library, arXiv.org 20.10.2020
Subjects	Mathematics - Number Theory
Online Access	Get full text

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Summary:	Some new results concerning the equation \(\sigma(N)=aM, \sigma(M)=bN\) are proved. As a corollary, there are only finitely many odd superperfect numbers with a fixed number of distinct prime factors.
ISSN:	2331-8422
DOI:	10.48550/arxiv.0803.0437