Numbers whose sum of divisors is twice the number plus 1
In mathematics, a quasiperfect number is a natural numbern for which the sum of all its divisors (the sum-of-divisors functionσ(n)) is equal to 2n + 1. Equivalently, n is the sum of its non-trivial divisors (that is, its divisors excluding 1 and n). No quasiperfect numbers have been found so far.
The quasiperfect numbers are the abundant numbers of minimal abundance (which is 1).
Theorems
If a quasiperfect number exists, it must be an oddsquare number greater than 1035 and have at least seven distinct prime factors.[1]
Related
For a perfect numbern the sum of all its divisors is equal to 2n.