Perfect Number


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perfect number

[′pər·fikt ′nəm·bər]
(mathematics)
An integer which equals the sum of all its factors other than itself.

Perfect Number

 

a positive integer that is equal to the sum of all its factors except itself. Examples of perfect numbers are 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14.

As early as the third century B.C., Euclid showed that even perfect numbers could be obtained from the formula 2p–l(2p – 1) when p and 2p – 1 are prime numbers. Approximately 20 even perfect numbers have been found in this way. As of 1976, no odd perfect numbers are known, and their existence remains an open question. Perfect numbers were first investigated by the Pythagoreans, who ascribed a special mystical meaning to such numbers and combinations of such numbers.

perfect number

equal in value to the sum of those natural numbers that are less than the given number but that also divide (with zero remainder) the given number. [Math.: EB, VII: 872]
See: Perfection
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