关于具有三个不同素因子的盈不完全数  

On Near-imperfect Numbers with Three Distinct Prime Divisors

作　　者：孙翠芳 陶甜甜 SUN Cuifang;TAO Tiantian(School of Mathematics and Statistics,Anhui Normal University,Wuhu,Anhui,241002,P.R.China)

机构地区：[1]安徽师范大学数学与统计学院,芜湖安徽241002

出　　处：《数学进展》2020年第5期573-595,共23页Advances in Mathematics（China）

基　　金：Supported by NSFC (No.11471017);the Natural Science Foundation of Anhui Higher Education Institutions of China (Nos.KJ2018A0304,KJ2019A0488)。

摘　　要：设ρ是可乘算术函数,定义为对每个素数方幂pα,ρ(pα)=pα-pα-1+pα-2-…+(-1)α.对正整数n,若2ρ(n)=n+d,其中d是n的真因子,则称n为盈因子是d的盈不完全数.本文得到了具有三个不同素因子的所有奇盈不完全数和部分偶盈不完全数.Let p be a multiplicative arithmetic function defined by ρ(pa)=pα-pα-1+pα-2-…+(-1)α for every prime power pα.A positive integer n is called a near-imperfect number with redundant divisor d if 2ρ(n)=n+d,where d is a proper divisor of n.In this paper,we obtain all odd near-imperfect numbers and some even near-imperfect numbers with three distinct prime divisors.

关 键 词：盈不完全数 盈因子 可乘算术函数 

分 类 号：O156.1[理学—数学]