In mathematics, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors.

The first few semiperfect numbers are 6, 12, 18, 20, 24, 28, 30, 36, 40, ... ; every multiple of a semiperfect number is semiperfect, and every number of the form 2^mp for a natural number m and a prime number p such that 2^m < p < 2^{m + 1} is also semiperfect.

A semiperfect number that is equal to the sum of all its proper divisors is called a perfect number; an abundant number which is not semiperfect is called a weird number.

See also

• deficient number
• primitive semiperfect number
• quasiperfect number

External link

• MathWorld: Semiperfect number