On the Sum of Reciprocals of Amicable Numbers

On the Sum of Reciprocals of Amicable Numbers

Two numbers \(m\) and \(n\) are considered amicable if the sum of their proper divisors, \(s(n)\) and \(s(m)\), satisfy \(s(n) = m\) and \(s(m) = n\). In 1981, Pomerance showed that the sum of the reciprocals of all such numbers, \(P\), is a constant. We obtain both a lower and an upper bound on the...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2010-12
Hauptverfasser: Bayless, Jonathan, Klyve, Dominic
Format: Artikel
Sprache:eng
Schlagworte:
Upper bounds
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Two numbers \(m\) and \(n\) are considered amicable if the sum of their proper divisors, \(s(n)\) and \(s(m)\), satisfy \(s(n) = m\) and \(s(m) = n\). In 1981, Pomerance showed that the sum of the reciprocals of all such numbers, \(P\), is a constant. We obtain both a lower and an upper bound on the value of \(P\).
ISSN:2331-8422