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 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. 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.

Setup

Follow the setup instructions for Crystal here:

http://exercism.io/languages/crystal

More help installing can be found here:

http://crystal-lang.org/docs/installation/index.html

Making the Test Suit Pass

Execute the tests with:

$ crystal spec

In each test suite all but the first test have been skipped.

Once you get a test passing, you can unskip the next one by changing pending to it.

Source

Taken from Chapter 2 of Functional Thinking by Neal Ford. 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.

perfect_numbers