On arithmetic numbers

被引：0
|
作者：
Oller-Marcen, Antonio M. [1 ]
机构：
[1] Ctr Univ Def Zaragoza, Zaragoza 50090, Spain
来源：
MATHEMATISCHE NACHRICHTEN | 2015年 / 288卷 / 5-6期
关键词：
Arithmetic number; prime power; mean of divisors; 11A25; 11B99;
D O I：
10.1002/mana.201400085
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
An integer n is said to be arithmetic if the arithmetic mean of its divisors is an integer. In this paper, using properties of the factorization of values of cyclotomic polynomials, we characterize arithmetic numbers. As an application, we give an interesting characterization of Mersenne numbers.
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页码：665 / 669
页数：5
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