In mathematics, a semiperfect number (also called a pseudoperfect number) is a natural number n that is equal to the sum of all or some of its proper divisors (the divisor function σ(n)). The first few semiperfect numbers are 6, 12, 18, 20, 24, 28, 30, 36, 40, ... (Sloane's A005835); every multiple of a semiperfect number is semiperfect, and every number of the form 2mp for a natural number m and a prime number 2m < p < 2m + 1 is also semiperfect.
Semiperfect numbers that are equal to the sum of all their proper divisors are called perfect number; an abundant number which is not semiperfect is called a weird number.
