Semiperfect number

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 2^mp for a natural number m and a prime number 2^m < p < 2^{m + 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.

Also see

• Primitive semiperfect number
• Quasiperfect number
• Deficient number

External links

• MathWorld: Semiperfect number