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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.
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