# Definition:Quasiperfect Number

Jump to navigation Jump to search

## Definition

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

### Definition 1

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

$n$ is quasiperfect if and only if $A \left({n}\right) = 1$.

### Definition 2

$n$ is quasiperfect if and only if:

$\sigma \left({n}\right) = 2 n + 1$

where $\sigma \left({n}\right)$ denotes the $\sigma$ function of $n$.

### Definition 3

$n$ is quasiperfect if and only if it is exactly one less than the sum of its aliquot parts.

## Also known as

Some sources use the terms:

• Quasi-perfect
• Slightly excessive

## Also see

• Results about quasiperfect numbers can be found here.