Perfect number

Definition

A positive integer $n$ is perfect if it is equal to the sum of its positive divisors other than $n$. Equivalently, $\sigma(n) = 2n$, where $\sigma$ is the sum of divisors.

Remarks

The first perfect numbers are $6$, $28$, $496$ and $8128$. For example, $28 = 1 + 2 + 4 + 7 + 14$. The Euclid–Euler theorem describes all even perfect numbers by Mersenne primes. No odd perfect number is known, and it is an open problem whether one exists.

Explanations

L1 human

A perfect number is the sum of its smaller divisors. The divisors of $6$ other than $6$ are $1$, $2$ and $3$, and $1 + 2 + 3 = 6$.