Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 SuperperfectNumberQ

Source Notebook

Check whether a number is a superperfect number

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["SuperperfectNumberQ"][n]

checks whether n is a superperfect number.

ResourceFunction["SuperperfectNumberQ"][n,m,k]

checks whether n is an (m,k)-superperfect number.

Details and Options

A number x is considered superperfect if it is equal to half the sum of the divisors of the sum of its divisors, i.e. if it satisfies Total@Divisors@Total@Divisors@x⩵2*x.
A number x is considered (m, k)-superperfect if it satisfies Nest[DivisorSigma[1,#]&,x,m]⩵k*x.

Examples

Basic Examples (3) 

Check whether 16 is superperfect:

In[1]:=
ResourceFunction["SuperperfectNumberQ"][16]
Out[1]=

Check whether 10 is superperfect:

In[2]:=
ResourceFunction["SuperperfectNumberQ"][10]
Out[2]=

Check whether 15 is (3,3)-superperfect:

In[3]:=
ResourceFunction["SuperperfectNumberQ"][15, 3, 3]
Out[3]=

Publisher

Wolfram|Alpha Math Team

Version History

  • 3.0.0 – 23 March 2023
  • 2.0.0 – 29 April 2020
  • 1.0.0 – 17 April 2020

Related Resources

License Information