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.

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. https://mathworld.wolfram.com/PseudoperfectNumber.html