# Definition:Untouchable Number

## Definition

An untouchable number is a (strictly) positive integer that is not the aliquot sum of any integer.

### Sequence

The sequence of untouchable numbers begins:

$2, 5, 52, 88, 96, 120, 124, 146, 162, 188, 206, 210, 216, 238, 246, 248, 262, \ldots$

## Also known as

Untouchable numbers are also known as nonaliquot numbers.

## Historical Note

The concept of an untouchable number was invented by Paul Erdős.