26 lines
1.6 KiB
Markdown
26 lines
1.6 KiB
Markdown
# 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**.
|
|
|
|
## 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.
|
|
|