perfect-numbers: description clarification (#518)

* perfect-numbers: description clarification

- add links to aliquot sum and Nicomachus
- provide examples of perfect, abundant, and deficient numbers
- provide instruction statement at bottom

* perfect-numbers: reorder text

- move aliquot sum section down

Author: rootulp

exercises/perfect-numbers/description.md

@@ -1,20 +1,13 @@
-The Greek mathematican Nicomachus devised a classification scheme for
-natural numbers, identifying each as belonging uniquely to the
-categories of _abundant_, _perfect_, or _deficient_.  A perfect number
-equals the sum of its positive divisors — the pairs of numbers whose
-product yields the target number, excluding the number itself.
-
-- Perfect: Sum of factors = number
-- Abundant: Sum of factors > number
-- Deficient: Sum of factors < number
-
-The Aliquot sum is defined as the sum of the factors of a number not
-including the number itself.
-
-## Examples
-
-- 6 is a perfect number because its divisors are 1, 2, 3 and 6 = 1 + 2 +
-  3.
-- 28 is a perfect number because 28 = 1 + 2 + 4 + 7 + 14.
-- Prime numbers 7, 13, etc are considered deficient in the Nicomachus
-  classification.
+The Greek mathematican [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 whethether a given number is **abundant** or **deficient**.