In mathematics, a semiperfect number or pseudoperfect number is a natural numbern 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 2mp for a natural number m and a prime numberp such that 2m < p < 2m + 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.
Just as the theorem on multiples of abundant numbers shows that multiples of abundant numbers are also abundant, it is also true that multiples of semiperfectnumbers are also semiperfect, and T. Foregger's proof of the abundant number theorem lays bare a simple mechanism that we can also employ for semiperfectnumbers.
"positive multiple of a semiperfectnumber is also semiperfect" is owned by Mravinci.
This is version 1 of positive multiple of a semiperfectnumber is also semiperfect, born on 2006-10-10.
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