A number is perfect if sigma(n) = 2n, or, equivalently, if (n) = 2. Another way of saying this is that sum of the proper divisors of n equals n. Contrast abundant, deficient. Every multiple of a perfect number other than itself is abundant, and every proper divisor is deficient. A Mersenne prime multiplied by the preceding power of two is a perfect number; i.e., if 2^p - 1 is prime, then (2^p - 1)*2^(p - 1) is perfect. All even perfect numbers are of this form; it is not known if there any odd perfect numbers.