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.

Also see

• Infinite Number of Untouchable Numbers, as proved by Paul Erdős
• Odd Untouchable Numbers

Historical Note

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

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $5$
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $52$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $5$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $52$

• Weisstein, Eric W. "Untouchable Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/UntouchableNumber.html