Semiperfect number

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, ... (sequence A005835 in OEIS); 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