# Definition:Deficient Number

## 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 deficient if and only if $A \left({n}\right) < 0$.

### Definition 2

Let $\sigma \left({n}\right)$ be the sigma function of $n$.

$n$ is deficient if and only if:

$\dfrac {\sigma \left({n}\right)} n < 2$

### Definition 3

$n$ is deficient if and only if it is greater than its aliquot sum.

## Sequence

The sequence of deficient numbers begins:

$2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, \ldots$

## Also see

• Results about deficient numbers can be found here.