# Superabundant number

From 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 is termed a **superabundant number** if it is a strict maximum-so-far for the ratio , where 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.