improved perfect number algorithm in maths module

maths/perfect_number.py

@@ -1,86 +1,27 @@
-"""
-== Perfect Number ==
-In number theory, a perfect number is a positive integer that is equal to the sum of
-its positive divisors, excluding the number itself.
-For example: 6 ==> divisors[1, 2, 3, 6]
-    Excluding 6, the sum(divisors) is 1 + 2 + 3 = 6
-    So, 6 is a Perfect Number
-
-Other examples of Perfect Numbers: 28, 486, ...
-
-https://en.wikipedia.org/wiki/Perfect_number
-"""
-
-
-def perfect(number: int) -> bool:
+def is_perfect_number(n: int) -> bool:
     """
-    Check if a number is a perfect number.
+    Check whether a number is a Perfect Number.
 
-    A perfect number is a positive integer that is equal to the sum of its proper
-    divisors (excluding itself).
+    A perfect number is a positive integer that is equal to the sum
+    of its proper positive divisors (excluding itself).
 
-    Args:
-        number: The number to be checked.
-
-    Returns:
-        True if the number is a perfect number otherwise, False.
-    Start from 1 because dividing by 0 will raise ZeroDivisionError.
-    A number at most can be divisible by the half of the number except the number
-    itself. For example, 6 is at most can be divisible by 3 except by 6 itself.
-    Examples:
-    >>> perfect(27)
-    False
-    >>> perfect(28)
-    True
-    >>> perfect(29)
-    False
-    >>> perfect(6)
+    >>> is_perfect_number(6)
     True
-    >>> perfect(12)
-    False
-    >>> perfect(496)
-    True
-    >>> perfect(8128)
-    True
-    >>> perfect(0)
-    False
-    >>> perfect(-1)
-    False
-    >>> perfect(33550336)  # Large perfect number
+    >>> is_perfect_number(28)
     True
-    >>> perfect(33550337)  # Just above a large perfect number
-    False
-    >>> perfect(1)  # Edge case: 1 is not a perfect number
+    >>> is_perfect_number(10)
     False
-    >>> perfect("123")  # String representation of a number
-    Traceback (most recent call last):
-    ...
-    ValueError: number must be an integer
-    >>> perfect(12.34)
-    Traceback (most recent call last):
-      ...
-    ValueError: number must be an integer
-    >>> perfect("Hello")
-    Traceback (most recent call last):
-      ...
-    ValueError: number must be an integer
     """
-    if not isinstance(number, int):
-        raise ValueError("number must be an integer")
-    if number <= 0:
+    if n <= 1:
         return False
-    return sum(i for i in range(1, number // 2 + 1) if number % i == 0) == number
-
-
-if __name__ == "__main__":
-    from doctest import testmod
 
-    testmod()
-    print("Program to check whether a number is a Perfect number or not...")
-    try:
-        number = int(input("Enter a positive integer: ").strip())
-    except ValueError:
-        msg = "number must be an integer"
-        raise ValueError(msg)
+    divisors_sum = 1
+    i = 2
+    while i * i <= n:
+        if n % i == 0:
+            divisors_sum += i
+            if i != n // i:
+                divisors_sum += n // i
+        i += 1
 
-    print(f"{number} is {'' if perfect(number) else 'not '}a Perfect Number.")
+    return divisors_sum == n