# 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**.

## Rust Installation

Refer to the [exercism help page][help-page] for Rust installation and learning
resources.

## Writing the Code

Execute the tests with:

```bash
$ cargo test
```

All but the first test have been ignored. After you get the first test to
pass, open the tests source file wich is located in the `tests` directory
and remove the `#[ignore]` flag from the next test and get the tests to pass
again. Each separate test is a function with `#[test]` flag above it.
Continue, until you pass every test. 

If you wish to run all tests without editing the tests source file, use:

```bash
$ cargo test -- --ignored
```

To run a specific test, for example `some_test`, you can use:

```bash
$ cargo test some_test
```

If the specfic test is ignored use:

```bash
$ cargo test some_test -- --ignored
```

To learn more about Rust tests refer to the [online test documentation][rust-tests]

Make sure to read the [Modules](https://doc.rust-lang.org/book/second-edition/ch07-00-modules.html) chapter if you
haven't already, it will help you with organizing your files.

## Feedback, Issues, Pull Requests

The [exercism/rust](https://github.com/exercism/rust) repository on GitHub is the home for all of the Rust exercises. If you have feedback about an exercise, or want to help implement new exercises, head over there and create an issue. Members of the rust track team are happy to help!

If you want to know more about Exercism, take a look at the [contribution guide](https://github.com/exercism/docs/blob/master/contributing-to-language-tracks/README.md).

[help-page]: http://exercism.io/languages/rust
[modules]: https://doc.rust-lang.org/book/second-edition/ch07-00-modules.html
[cargo]: https://doc.rust-lang.org/book/second-edition/ch14-00-more-about-cargo.html
[rust-tests]: https://doc.rust-lang.org/book/second-edition/ch11-02-running-tests.html

## 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.