# a 01 Integers 9 ( 2009 ) , 1 - 8 on K - Imperfect Numbers
نویسندگان
چکیده
A positive integer n is called a k-imperfect number if kρ(n) = n for some integer k ! 2, where ρ is a multiplicative arithmetic function defined by ρ(pa) = pa−pa−1+pa−2−· · ·+ (−1)a for a prime power pa. In this paper, we prove that every odd k-imperfect number greater than 1 must be divisible by a prime greater than 102, give all k-imperfect numbers less than 232 = 4294 967 296, and give several necessary conditions for the existence of an odd k-imperfect number.
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