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Encyclopedia > Quasiperfect number

In mathematics, a quasiperfect number is a natural number n for which the sum of all its divisors (the divisor function σ(n)) is equal to 2n + 1. Quasiperfect numbers are abundant numbers. No quasiperfect numbers have been found so far, but it has been shown that if any quasiperfect numbers exist, they must be greater than 1035 and have at least seven divisors.


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  Results from FactBites:
 
Article about "Perfect number" in the English Wikipedia on 24-Apr-2004 (607 words)
Thus, 6 is a perfect number, because 1, 2 and 3 are its proper positive divisors and 1 + 2 + 3 = 6.
Numbers where the sum is less than the number itself are called deficient, and where it is greater, abundant.
A pair of numbers which are the sum of each other's proper divisors are called amicable, and larger cycles of numbers are called sociable.
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