[Sync Iteration] python/perfect-numbers/2

solutions/python/perfect-numbers/2/perfect_numbers.py

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+"""
+Determine if a number is perfect, abundant, or deficient based on
+Nicomachus' (60 - 120 CE) classification scheme for positive integers.
+"""
+
+import math
+
+
+def classify(number: int) -> str:
+    """
+    A perfect number equals the sum of its positive divisors.
+
+    :param number: int a positive integer
+    :return: str the classification of the input integer
+    """
+    if number < 1:
+        raise ValueError(
+            "Classification is only possible for positive integers."
+        )
+
+    total_divisors: int = 1
+
+    for n in range(2, int(math.sqrt(number)) + 1):
+        if number % n == 0:
+            total_divisors += n
+            if n != number // n:
+                total_divisors += number // n
+
+    if number == 1 or number > total_divisors:
+        return "deficient"
+
+    if total_divisors == number:
+        return "perfect"
+
+    return "abundant"