# Definition:Semiperfect Number

Jump to navigation
Jump to search

## 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.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $20$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $20$

- Weisstein, Eric W. "Pseudoperfect Number." From
*MathWorld*--A Wolfram Web Resource. http://mathworld.wolfram.com/PseudoperfectNumber.html