Add function to check abundant numbers

DIRECTORY.md

@@ -772,6 +772,7 @@
   * [Solovay Strassen Primality Test](maths/solovay_strassen_primality_test.py)
   * [Spearman Rank Correlation Coefficient](maths/spearman_rank_correlation_coefficient.py)
   * Special Numbers
+    * [Abundant Numbers](maths/special_numbers/abundant_numbers.py)
     * [Armstrong Numbers](maths/special_numbers/armstrong_numbers.py)
     * [Automorphic Number](maths/special_numbers/automorphic_number.py)
     * [Bell Numbers](maths/special_numbers/bell_numbers.py)

maths/special_numbers/abundant_numbers.py

@@ -0,0 +1,55 @@
+"""
+A number n is said to be an Abundant number if
+the sum of its proper divisors is greater than the number itself.
+
+Examples of Abundant Numbers: 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, ...
+"""
+
+
+def is_abundant_number(number: int) -> bool:
+    """
+    This function takes an integer number as input.
+    Returns True if the number is an abundant number.
+
+    >>> is_abundant_number(-1)
+    False
+    >>> is_abundant_number(0)
+    False
+    >>> is_abundant_number(12)
+    True
+    >>> is_abundant_number(18)
+    True
+    >>> is_abundant_number(28)
+    False
+    >>> is_abundant_number(20)
+    True
+    >>> is_abundant_number(6)
+    False
+    >>> is_abundant_number(1)
+    False
+    >>> is_abundant_number(945)
+    True
+    >>> is_abundant_number(28.0)
+    Traceback (most recent call last):
+        ...
+    TypeError: Input value of [number=28.0] must be an integer
+    """
+    if not isinstance(number, int):
+        msg = f"Input value of [number={number}] must be an integer"
+        raise TypeError(msg)
+    if number < 1:
+        return False
+
+    divisor_sum = 1  # 1 is always a proper divisor
+    for i in range(2, int(number**0.5) + 1):
+        if number % i == 0:
+            divisor_sum += i
+            if i != number // i:
+                divisor_sum += number // i
+    return divisor_sum > number
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()