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 $n$ such that $n$ 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 $n$ is a perfect number.

Relation with other properties

Stronger properties

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