Function Repository Resource:

# AbundantNumberQ

Check whether an input is an abundant number

Contributed by: Wolfram|Alpha Math Team
 ResourceFunction["AbundantNumberQ"][n] checks whether the sum of the proper divisors of the integer n is greater than n.

## Details and Options

An abundant number is a number whose sum of proper divisors is greater than the number itself. The proper divisors of an integer n are the positive integers less than n that divide n.
If a number's divisor sum is less than or equal to its value, then it is called deficient or perfect, respectively.

## Examples

### Basic Examples (2)

Check whether 5 is abundant:

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Check whether 12 is abundant:

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### Properties and Relations (2)

For noninteger input, AbundantNumberQ returns False:

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Prime numbers are never abundant:

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## Publisher

Wolfram|Alpha Math Team

## Version History

• 2.0.0 – 23 March 2023
• 1.0.0 – 10 April 2020