Pseudoperfect number: Difference between revisions
(Created page with '{{natural number property}} ==Definition== A '''pseudoperfect number''' is a natural number <math>n</math> such that <math>n</math> equals the sum of a subset of the set of...') |
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* [[Weaker than::Perfect number]]: This requires <math>n</math> to be precisely equal to the sum of all its positive proper divisors. | * [[Weaker than::Perfect number]]: This requires <math>n</math> to be precisely equal to the sum of all its positive proper divisors. | ||
* [[Weaker than::Quasiperfect number]]: This requires <math>n</math> to be precisely equal to the sum of all its positive proper ''nontrivial'' divisors. | * [[Weaker than::Quasiperfect number]]: This requires <math>n</math> to be precisely equal to the sum of all its positive proper ''nontrivial'' divisors. | ||
==External links== | |||
* [[Mathworld:PseudoperfectNumber|Pseudoperfect number on Mathworld]] | |||
Latest revision as of 14:29, 5 May 2009
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.