An integer that is equal to the sum of its positive divisors (not including itself). Thus, 6 is a perfect number, since its positive divisors (not including itself) are 1, 2, and 3, and 1 + 2 + 3 = 6; so too are 28 and 496, for example. At present there are over 50 known perfect numbers, all even. If 2^p−1 is prime (so that it is a Mersenne prime), then 2^p−1(2^p−1) is perfect; moreover, these are the only even perfect numbers. It is an open problem whether an odd perfect number exists.

https://mathshistory.st-andrews.ac.uk/HistTopics/Perfect_numbers A brief history of perfect numbers.