# 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 tests

Execute the tests with:

```bash
$ elixir perfect_numbers_test.exs
```

### Pending tests

In the test suites, all but the first test have been skipped.

Once you get a test passing, you can unskip the next one by
commenting out the relevant `@tag :pending` with a `#` symbol.

For example:

```elixir
# @tag :pending
test "shouting" do
  assert Bob.hey("WATCH OUT!") == "Whoa, chill out!"
end
```

Or, you can enable all the tests by commenting out the
`ExUnit.configure` line in the test suite.

```elixir
# ExUnit.configure exclude: :pending, trace: true
```

For more detailed information about the Elixir track, please
see the [help page](http://exercism.io/languages/elixir).

## 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.