含有2个不同素因子的k-盈不完全数

k-near-imperfect Numbers with Two Distinct Prime Divisors

设p为质数,α为正整数,对于素数方幂p^(α),令ρ(p^(α))=p^(α)-p^(α-1)+p^(α-2)-…+(-1)^(α).给出方程kρ(n)=n+d(k=3,4)的全部正整数解,其中,n只有2个不同素因子数,1≤d<n且d|n.

Let p be a prime andαbe a positive integer.For any given prime power p^(α),letρ(p^(α))=p^(α)-p^(α-1)+p^(α-2)-…+(-1)^(α).We give all positive integer solutions of the equation kρ(n)=n+d(k=3,4),where n is a positive integer with exact two distinct prime divisors,1≤d<n and d|n.