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# Perfect Numbers

Determine if a number is perfect, abundant, or deficient based on
Nicomachus' (60 - 120 CE) classification scheme for natural numbers.

The Greek mathematician [Nicomachus](https://en.wikipedia.org/wiki/Nicomachus) devised a classification scheme for natural numbers, identifying each as belonging uniquely to the categories of **perfect**, **abundant**, or **deficient** based on their [aliquot sum](https://en.wikipedia.org/wiki/Aliquot_sum). The aliquot sum is defined as the sum of the factors of a number not including the number itself. For example, the aliquot sum of 15 is (1 + 3 + 5) = 9

- **Perfect**: aliquot sum = number 
  - 6 is a perfect number because (1 + 2 + 3) = 6
  - 28 is a perfect number because (1 + 2 + 4 + 7 + 14) = 28
- **Abundant**: aliquot sum > number
  - 12 is an abundant number because (1 + 2 + 3 + 4 + 6) = 16
  - 24 is an abundant number because (1 + 2 + 3 + 4 + 6 + 8 + 12) = 36
- **Deficient**: aliquot sum < number
  - 8 is a deficient number because (1 + 2 + 4) = 7
  - Prime numbers are deficient
  
Implement a way to determine whether a given number is **perfect**. Depending on your language track, you may also need to implement a way to determine whether a given number is **abundant** or **deficient**.

## Running the tests

To run the tests, run the command `busted .` from within the exercise directory.

## Further information

For more detailed information about the Lua track, including how to get help if
you're having trouble, please visit the exercism.io [Lua language page](http://exercism.io/languages/lua/about).

## Source

Taken from Chapter 2 of Functional Thinking by Neal Ford. [http://shop.oreilly.com/product/0636920029687.do](http://shop.oreilly.com/product/0636920029687.do)

## Submitting Incomplete Solutions
It's possible to submit an incomplete solution so you can see how others have completed the exercise.

Version data entries

53 entries across 53 versions & 1 rubygems

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trackler-2.2.1.27 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.26 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.25 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.24 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.23 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.22 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.21 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.20 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.19 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.18 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.17 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.16 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.15 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.14 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.13 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.12 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.11 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.10 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.9 tracks/lua/exercises/perfect-numbers/README.md
trackler-2.2.1.8 tracks/lua/exercises/perfect-numbers/README.md