Abundant 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 an abundant number if $\sigma (n)>2n$. Here, $\sigma$ denotes the divisor sum function, or the sum of all positive divisors of $n$. Equivalently, $n$ is abundant if the sum of all proper divisors of $n$ is strictly greater than $n$.

Relation with other properties

Opposite properties

• Perfect number
• Deficient number