Add function to check deficient numbers

DIRECTORY.md

@@ -777,6 +777,7 @@
     * [Bell Numbers](maths/special_numbers/bell_numbers.py)
     * [Carmichael Number](maths/special_numbers/carmichael_number.py)
     * [Catalan Number](maths/special_numbers/catalan_number.py)
+    * [Deficient Numbers](maths/special_numbers/deficient_numbers.py)
     * [Hamming Numbers](maths/special_numbers/hamming_numbers.py)
     * [Happy Number](maths/special_numbers/happy_number.py)
     * [Harshad Numbers](maths/special_numbers/harshad_numbers.py)

maths/special_numbers/deficient_numbers.py

@@ -0,0 +1,58 @@
+"""
+A number n is said to be a Deficient number if
+the sum of its proper divisors is less than the number itself.
+
+Examples of Deficient Numbers: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, ...
+"""
+
+
+def is_deficient_number(number: int) -> bool:
+    """
+    This function takes an integer number as input.
+    Returns True if the number is a deficient number.
+
+    >>> is_deficient_number(-1)
+    False
+    >>> is_deficient_number(0)
+    False
+    >>> is_deficient_number(1)
+    True
+    >>> is_deficient_number(2)
+    True
+    >>> is_deficient_number(6)
+    False
+    >>> is_deficient_number(12)
+    False
+    >>> is_deficient_number(7)
+    True
+    >>> is_deficient_number(28)
+    False
+    >>> is_deficient_number(15)
+    True
+    >>> is_deficient_number(8.0)
+    Traceback (most recent call last):
+        ...
+    TypeError: Input value of [number=8.0] 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
+    if number == 1:
+        return True
+
+    divisor_sum = 1
+    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()