I'm really confused about these two. For example if $n = 6$, then:
Divisors: $2, 3$
Proper Divisors: $1, 2, 3, 6$
Is it right?
From Elementary Number Theory and Its Application by Kenneth H. Rosen 6th edition, page 256:
Because of certain mystical beliefs, the ancient Greeks were interested in those integers that are equal to the sum of all their proper positive divisors. Such integers are called perfect numbers.
$\sigma(6) = 1 + 2 + 3 + 6 = 12$, we see that $6$ is perfect.