含有两个不同素因子的盈不完全数  

On near-imperfect numbers with two distinct prime divisors

作　　者：陶甜甜 孙翠芳 TAO Tiantian;SUN Cuifang(School of Mathematics and Statistics, Anhui Normal University, Wuhu 241003, China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241003

出　　处：《中国科学技术大学学报》2019年第9期704-710,共7页JUSTC

基　　金：the National Natural Science Foundation of China(11471017);the Natural Science Foundation of Anhui Higher Education Institutions of China(KJ2018A0304,KJ2019A0488).

摘　　要：对于素数方幂p^α,设可乘函数ρ(p^α)=p^α-p^α-1+p^α-2-…+(-1)α.称满足条件2ρ(n)=n+d的正整数n为盈不完全数,其中d是n的真因子.给出了含有两个不同素因子的所有盈不完全数.Letρbe a multiplicative arithmetic function defined byρ(p^α)=p^α-p^α-1+p^α-2-…+(-1)αfor every prime power p^α.For a positive integer n,n is called a near-imperfect number if 2ρ(n)=n+d where d is a proper divisor of n.Here all near-imperfect numbers with two distinct prime divisors were obtained.

关 键 词：盈不完全数 素因子 可乘函数 

分 类 号：O156[理学—数学]