一类正整数是否是孤立数的讨论  

Discussion on a Kind of Positive Integers Are Anti-sociable Number or Not

作　　者：张四保 伊尔夏提·吐尔贡 姜莲霞 ZHANG Si-bao;Yierxiati-Tuergong;JIANG Lian-xia(School of Mathematics and Statistics,Kashi University,Kashi 844000,China;School of Computer Science and Technology,Kashi University,Kashi 844000,China)

机构地区：[1]喀什大学数学与统计学院,新疆喀什844000 [2]喀什大学计算机科学与技术学院,新疆喀什844000

出　　处：《数学的实践与认识》2022年第11期276-280,共5页Mathematics in Practice and Theory

基　　金：新疆维吾尔自治区自然科学基金资助项目(2022D01A14)。

摘　　要：对于任意正整数n,令σ(n)表示为n的所有正因数的和函数.对于正整数n,若存在正整数m满足关系式σ(n)=σ(m)=n+m,则称正整数数对(n,m)为一对亲和数;若不存在正整数m满足关系式σ(n)=σ(m)=n+m,则称n为孤立数.亲和数与孤立数是数论中的两类重要的整数.利用初等方法结合计算机python语言,证明了整数E(33,t)=1/2(33^(2^(t))+1)是孤立数.For any positive integer n,let σ(n) be the sum of all positive factors of n.For positive integer n,if there is a positive integer m satisfied the relationship σ(n)=σ(m)=n+m,then the positive integer number pair(n,m) is called amicable pair;If there is no positive integer msatisfied the relation σ(n) =σ(m) =n+m,then the positive integer n called an anti-sociable number.Amicable pair and anti-sociable number are two important integers in number theory.By using elementary method and the computer python language,the positive integer E(33,t)=1/2(33^(2^(t))+1) is an anti-sociable number was proved.

关 键 词：亲和数 孤立数 初等方法 

分 类 号：O156[理学—数学]