形如2^(α-1)p_1p_2p_3的near-perfect数

Near-perfect Numbers of the Form n = 2^(α-1)p_1p_2p_3

设α是正整数且α≥2,p_1、p_2、p_3是不同的奇素数.利用初等数论的方法和技巧给出了形如n=2^(α-1)p_1p_2p_3的near-perfect数的一种判别方法,以及从已知near-perfect数中构造新near-perfect数的一种方法.

Let α≥2 be a positive integer and p1,p2,p3 be distinct odd primes.By elementary methods and techniques of number theory,in this paper we give a criterion for near-perfect numbers in the form n = 2^α-1 p1 p2 p3 and a construction for near-perfect numbers based on some known near-perfect numbers.