A short interval result for the exponential divisor function 1

A short interval result for the exponential divisor function 1

The integer d = Π^sup s^^sub i=1^P^sup b^sub i^^^sub i^ is called an exponential divisor of n = Π^sup s^^sub i=1^P^sup a^sub i^^^sub i^ if b^sub i^|a^sub i^ for every i ∈ 1,2,...,s. Let τ^sup (e)^(n) denote the number of exponential divisors of n, where τ^sup (e)^(1) = 1 by convention. In this paper...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Scientia magna 2009-10, Vol.5 (4), p.52-52
Hauptverfasser: Wang, Jian, Zheng, Chenghua
Format: Artikel
Sprache:eng
Schlagworte:
Mathematical functions
Numbers
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:The integer d = Π^sup s^^sub i=1^P^sup b^sub i^^^sub i^ is called an exponential divisor of n = Π^sup s^^sub i=1^P^sup a^sub i^^^sub i^ if b^sub i^|a^sub i^ for every i ∈ 1,2,...,s. Let τ^sup (e)^(n) denote the number of exponential divisors of n, where τ^sup (e)^(1) = 1 by convention. In this paper we shall establish a short interval result for r-th power of the function τ^sup (e)^ where r ≥ 1 is a fixed integer. [PUBLICATION ABSTRACT]
ISSN:1556-6706