Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 AbundantNumberQ

Source Notebook

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:

In[1]:=
ResourceFunction[ "AbundantNumberQ", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][5]
Out[1]=

Check whether 12 is abundant:

In[2]:=
ResourceFunction[ "AbundantNumberQ", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][12]
Out[2]=

Properties and Relations (2) 

For noninteger input, AbundantNumberQ returns False:

In[3]:=
ResourceFunction[ "AbundantNumberQ", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"]["a"]
Out[3]=
In[4]:=
ResourceFunction[ "AbundantNumberQ", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"][3.8]
Out[4]=

Prime numbers are never abundant:

In[5]:=
ResourceFunction[ "AbundantNumberQ", ResourceSystemBase -> "https://www.wolframcloud.com/obj/resourcesystem/api/1.0"] /@ Prime /@ Range[10]
Out[5]=

Publisher

Wolfram|Alpha Math Team

Version History

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

Related Resources

License Information