perfect number | Definition & Facts
Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128. The discovery of such numbers is lost in prehistory. It is known, however, that the Pythagoreans (founded c. 525 bce) studied perfect numbers for their “mystical” properties. The mystical tradition was continued by the Neo-Pythagorean philosopher Nicomachus of Gerasa (fl. c. 100 ce), who classified numbers as deficient, perfect, and superabundant according to whether the sum of their divisors wa...