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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**.
## Making the Test Suite Pass
1. Get [PHPUnit].
% wget --no-check-certificate https://phar.phpunit.de/phpunit.phar
% chmod +x phpunit.phar
2. Execute the tests for an assignment.
% phpunit.phar wordy/wordy_test.php
[PHPUnit]: http://phpunit.de
## 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.
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