# 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**.


## Getting Started

For installation and learning resources, refer to the
[exercism help page](http://exercism.io/languages/haskell).

## Running the tests

To run the test suite, execute the following command:

```bash
stack test
```

#### If you get an error message like this...

```
No .cabal file found in directory
```

You are probably running an old stack version and need
to upgrade it.

#### Otherwise, if you get an error message like this...

```
No compiler found, expected minor version match with...
Try running "stack setup" to install the correct GHC...
```

Just do as it says and it will download and install
the correct compiler version:

```bash
stack setup
```

## Running *GHCi*

If you want to play with your solution in GHCi, just run the command:

```bash
stack ghci
```

## Feedback, Issues, Pull Requests

The [exercism/haskell](https://github.com/exercism/haskell) repository on
GitHub is the home for all of the Haskell exercises.

If you have feedback about an exercise, or want to help implementing a new
one, head over there and create an issue.  We'll do our best to help you!

## 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.