# Definition:Almost Perfect Number

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## Contents

## 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 **almost perfect** if and only if $A \left({n}\right) = -1$.

### Definition 2

$n$ is **almost perfect** 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 **almost perfect** if and only if it is exactly one greater than the sum of its aliquot parts.

Thus an **almost perfect number** can be described as "deficient, but only just".

## Also known as

An **almost perfect number** is also known as:

- a
**least deficient number** - a
**slightly defective number**.

Some sources hyphenate: **almost-perfect**.

## Sequence

The sequence of almost perfect numbers begins:

- $1, 2, 4, 8, 16, 32, 64, 128, \ldots$

## Examples

### $16$

- $16$ is an almost perfect number.

## Also see

- Results about
**almost perfect numbers**can be found here.

## Sources

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $32$