In number theory

Number theory

Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...

, a perfect number is a positive integer that is equal to the sum of its proper positive divisor

Divisor

In mathematics, a divisor of an integer n, also called a factor of n, is an integer which divides n without leaving a remainder.-Explanation:...

s, 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

Divisor function

In mathematics, and specifically in number theory, a divisor function is an arithmetical function related to the divisors of an integer. When referred to as the divisor function, it counts the number of divisors of an integer. It appears in a number of remarkable identities, including relationships...

(n) = 2n.
The first perfect number is 6, because 1, 2, and 3 are its proper positive divisors, and 1 + 2 + 3 = 6.