Deficient 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 deficient number if $\sigma (n)<2n$, where $\sigma$ denotes the divisor sum function. In other words, $n$ is greater than the sum of all its proper positive divisors.

Relation with other properties

Opposite properties

• Perfect number: This requires $\sigma (n)=2n$.
• Abundant number: This requires $\sigma (n)>2n$.

Stronger properties

• Almost perfect number: A natural number $n$ such that $\sigma (n)=2n-1$.