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.
To run the tests, run the command dotnet test from within the exercise directory.
Initially, only the first test will be enabled. This is to encourage you to solve the exercise one step at a time.
Once you get the first test passing, remove the Skip property from the next test and work on getting that test passing.
Once none of the tests are skipped and they are all passing, you can submit your solution
using exercism submit PerfectNumbers.cs
For more detailed information about the C# track, including how to get help if you're having trouble, please visit the exercism.io C# language page.
Taken from Chapter 2 of Functional Thinking by Neal Ford. http://shop.oreilly.com/product/0636920029687.do