Perfect number
Number theory
A positive integer equal to the sum of its proper divisors, meaning its positive divisors strictly less than itself. The smallest is 6 = 1 + 2 + 3.
What is usually left out
Euclid and Euler together established that the even perfect numbers are exactly the numbers 2ⁿ⁻¹(2ⁿ − 1) where 2ⁿ − 1 is prime, tying them one-to-one to the Mersenne primes. Whether any odd perfect number exists is open and has been for over two millennia, with no example found below 10¹⁵⁰⁰.
Related terms
In the atlas
- odd perfect number — Number theory, open