Improve documentation and clarify edge cases for aliquot sum algorithm

maths/aliquot_sum.nim

@@ -1,6 +1,15 @@
 ## Aliquot sum
+##
 ## In number theory, the aliquot sum s(n) of a positive integer n is the sum of
 ## all proper divisors of n, that is, all divisors of n other than n itself.
+##
+## For example:
+## - s(12) = 1 + 2 + 3 + 4 + 6 = 16
+## - s(1) = 0 (since 1 has no proper divisors)
+##
+## This function determines whether a positive integer is perfect (s(n) = n), abundant (s(n) > n), or deficient (s(n) < n).
+##
+## Reference:
 ## https://en.wikipedia.org/wiki/Aliquot_sum
 
 runnableExamples:
@@ -12,9 +21,16 @@ runnableExamples:
     echo fmt"The sum of all the proper divisors of {number} is {sum}"
 
 func aliquotSum*(number: Positive): Natural =
-  ## Returns the sum of all the proper divisors of the number
-  ## Example: aliquotSum(12) = 1 + 2 + 3 + 4 + 6 = 16
+  ## Compute the aliquot sum of a positive integer.
+  ##
+  ## Input:
+  ## - number: a positive integer (number > 0)
+  ## Output:
+  ## - The sum of all proper divisors of 'number'
+  ## Time Complexity: O(number)
+  ## Space Complexity: O(1)
   result = 0
+  # A proper divisor p satisfies `number = pq` with q greater than or equal to 2
   for divisor in 1 .. (number div 2):
     if number mod divisor == 0:
       result += divisor