Abstract: Let ρ be a multiplicative arithmetic function defined by ρ(pα)=pα-pα-1+pα-2-…+(-1)α for every prime power pα. 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.

Key words: near-imperfect number, prime divisor, multiplicative arithmetic function