It is most notable for being a perfect number, and one of the earliest numbers to be recognized as such. As a perfect number, it is tied to the Mersenne prime127, 27 - 1, with 26 ( 27 - 1 ) yielding 8,128. Also related to its being a perfect number, 8,128 is a harmonic divisor number.
Equivalently, a perfect number is a number that is half the sum of all of its positive divisors, or σ(n) = 2 n.
Numbers where the sum is less than the number itself are called deficient, and where it is greater than the number, abundant.
By definition, a perfect number is a fixed point of the restricted divisor function s(n) = σ(n) − n, and the aliquot sequence associated with a perfect number is a constant sequence.
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