Update aliquot_sum.py

Author: lighting9999

maths/aliquot_sum.py

@@ -1,33 +1,30 @@
 from __future__ import annotations
-
 import doctest
-from typing import overload, Tuple
-
+from typing import overload
 
 @overload
 def aliquot_sum(input_num: int) -> int: ...
 @overload
-def aliquot_sum(input_num: int, return_factors: bool) -> Tuple[int, list[int]]: ...
-
+def aliquot_sum(input_num: int, return_factors: bool) -> tuple[int, list[int]]: ...
 
 def aliquot_sum(
     input_num: int, return_factors: bool = False
-) -> int | Tuple[int, list[int]]:
+) -> int | tuple[int, list[int]]:
     """
-    Calculates the aliquot sum of a positive integer.
+    Calculates the aliquot sum of a positive integer. 
     The aliquot sum is the sum of all proper divisors of a number.
-
+    
     Args:
         input_num: Positive integer
         return_factors: If True, returns (sum, sorted_factor_list)
-
+    
     Returns:
         Aliquot sum or (sum, factors) if return_factors=True
-
+    
     Raises:
         TypeError: If input not integer
         ValueError: If input not positive
-
+        
     Examples:
         >>> aliquot_sum(15)
         9
@@ -39,16 +36,16 @@ def aliquot_sum(
         raise TypeError("Input must be an integer")
     if input_num <= 0:
         raise ValueError("Input must be positive integer")
-
+    
     # Special case: 1 has no proper divisors
     if input_num == 1:
         return (0, []) if return_factors else 0
-
+    
     # Initialize factors and total
     factors = [1]
     total = 1
     sqrt_num = int(input_num**0.5)
-
+    
     # Find factors efficiently
     for divisor in range(2, sqrt_num + 1):
         if input_num % divisor == 0:
@@ -58,18 +55,17 @@ def aliquot_sum(
             if complement != divisor:
                 factors.append(complement)
                 total += complement
-
+    
     factors.sort()
     return (total, factors) if return_factors else total
 
-
 def classify_number(n: int) -> str:
     """
     Classifies number based on aliquot sum:
     - Perfect: sum = number
     - Abundant: sum > number
     - Deficient: sum < number
-
+    
     Examples:
         >>> classify_number(6)
         'Perfect'
@@ -80,25 +76,24 @@ def classify_number(n: int) -> str:
         raise ValueError("Input must be positive integer")
     if n == 1:
         return "Deficient"
-
+    
     s = aliquot_sum(n)  # Always returns int
     if s == n:
         return "Perfect"
     return "Abundant" if s > n else "Deficient"
 
-
 if __name__ == "__main__":
     doctest.testmod()
-
+    
     print("Aliquot sum of 28:", aliquot_sum(28))
-
+    
     # Handle tuple return explicitly
     result = aliquot_sum(28, True)
     if isinstance(result, tuple):
         print("Factors of 28:", result[1])
-
+    
     print("Classification of 28:", classify_number(28))
-
+    
     # Large number test
     try:
         print("Aliquot sum for 10^9:", aliquot_sum(10**9))