# Definition:Semiperfect Number

## Definition

A semiperfect number is a positive integer which is equal to the sum of some or all of its aliquot parts.

### Sequence

The sequence of semiperfect numbers begins:

$6, 12, 18, 20, 24, 28, 30, \ldots$

## Also defined as

Some sources do not include the perfect numbers in the set of semiperfect numbers:

A semiperfect number is a positive integer which is equal to the sum of some, but not all of its aliquot parts.

It is possible this is a mistake in 1997: David Wells: Curious and Interesting Numbers (2nd ed.), as the author of this page has not been able to corroborate this definition with any sources elsewhere.

## Also known as

Some sources use a hyphen: semi-perfect number.

The term pseudoperfect is also often seen.

David Wells, possibly being jocular in his Curious and Interesting Numbers of $1986$, refers to such a number as pseudonymously pseudoperfect.

## Also see

• Results about semiperfect numbers can be found here.