# Pseudoperfect number

This article defines a property that can be evaluated for a natural number, i.e., every natural number either satisfies the property or does not satisfy the property.
View a complete list of properties of natural numbers

## Definition

A pseudoperfect number is a natural number  such that  equals the sum of a subset of the set of all its proper positive divisors. If that subset is the whole set of proper positive divisors, then  is a perfect number.

## Relation with other properties

### Stronger properties

• Perfect number: This requires  to be precisely equal to the sum of all its positive proper divisors.
• Quasiperfect number: This requires  to be precisely equal to the sum of all its positive proper nontrivial divisors.