I was reading the definition of what it means for a number to be perfect and I'm a little confused.
from Wikipedia:
a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum). Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself) i.e. σ1(n) = 2n.
But how can it be that a perfect number is one that is equal to the sum of its positive divisors , while at the same time being equal to half the sum of its positive divisors?
Best Answer
The first definition uses the term “proper” positive divisors. The word “proper” (which does not appear in the second definition) means “all divisors not including the number itself.”