Definition:Quasiperfect Number

Definition
Let $n \in \Z_{\ge 0}$ be a positive integer.

Let $A \left({n}\right)$ denote the abundance of $n$.

$n$ is quasiperfect iff $A \left({n}\right) = 1$.

Also known as
Some sources use the terms:


 * Quasi-perfect
 * Slightly excessive

Also see

 * Definition:Perfect Number
 * Definition:Almost Perfect
 * Definition:Abundance

Note
As of January 2014, there are no known quasiperfect numbers.

It has been proved, though, that if $n$ is a quasiperfect number, then:


 * $\omega \left({n}\right) \ge 7$


 * $n > 10^{35}$

where $\omega \left({n}\right)$ denotes the number of distinct prime factors of $n$.