In mathematics, an almost perfect number (sometimes also called slightly defective number) is a natural numbern such that the sum of all divisors of n (the divisor functionσ(n)) is equal to 2n _ 1. The only almost perfect numbers known are those of the form 2k for some natural number k; however, it has not been shown yet that all almost perfect numbers are of this form. Almost perfect numbers are deficient numbers.
In mathematics, a perfectnumber is defined as an integer which is the sum of its proper positive divisors, that is, the sum of the positive divisors not including the number.
Equivalently, a perfectnumber is a number that is half the sum of all of its positive divisors, or σ(n) = 2 n.
By definition, a perfectnumber is a fixed point of the restricted divisor function s(n) = σ(n) − n, and the aliquot sequence associated with a perfectnumber is a constant sequence.
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