Superabundant 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 natural number $n$ is termed a superabundant number if it is a strict maximum-so-far for the ratio $\sigma (n)/n$, where $\sigma$ denotes the divisor sum function.

Relation with other properties

• Highly composite number is a strict maximum-so-far for the closely related divisor count function.