Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 DeficientNumberQ

Source Notebook

Check whether an input is a deficient number

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["DeficientNumberQ"][n]

checks whether the sum of the proper divisors of the integer n is less than n.

Details and Options

A deficient number is a number whose sum of proper divisors is less 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 greater than or equal to its value, then it is called abundant or perfect, respectively.

Examples

Basic Examples (2) 

Check whether 5 is deficient:

In[1]:=
ResourceFunction["DeficientNumberQ"][5]
Out[1]=

Check whether 100 is deficient:

In[2]:=
ResourceFunction["DeficientNumberQ"][100]
Out[2]=

Properties and Relations (2) 

For non-integer input, DeficientNumberQ returns False:

In[3]:=
ResourceFunction["DeficientNumberQ"]["a"]
Out[3]=
In[4]:=
ResourceFunction["DeficientNumberQ"][3.8]
Out[4]=

All prime numbers are deficient:

In[5]:=
ResourceFunction["DeficientNumberQ"] /@ 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