, 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
)). 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 + 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.