Definition:Perfect Number

Also known as
The even perfect numbers are also known as the Euclid numbers.

However, on we already have a definition for Euclid number, as one more than a primorial.

As the only known perfect numbers are all even anyway, the distinction is rarely considered worthy of a separate definition.

Also see

 * Equivalence of Definitions of Perfect Number


 * Definition:Abundance
 * Definition:Abundancy Index


 * Definition:Deficient Number
 * Definition:Abundant Number


 * Definition:Almost Perfect Number
 * Definition:Quasiperfect Number


 * Theorem of Even Perfect Numbers: An even perfect number is of the form $2^{n - 1} \paren {2^n - 1}$, where $2^n - 1$ is prime.


 * Are All Perfect Numbers Even?


 * Definition:Mersenne Prime