Added file aliquot_sum.py (#1985)

* Added file aliquot_sum.py containing a function to find theo

* Added parameter type info to aliquot_sum.py

* Update maths/aliquot_sum.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Update maths/aliquot_sum.py

Co-authored-by: Christian Clauss <cclauss@me.com>

* Updated code to raise ValueErrors if input is bad

* Fixed logical operators

* Removed unnecessary import

* Updated aliquot_sum.py

* fixed formatting

* fixed documentation

Co-authored-by: Christian Clauss <cclauss@me.com>

maths/aliquot_sum.py

@@ -0,0 +1,46 @@
+def aliquot_sum(input_num: int) -> int:
+    """
+    Finds the aliquot sum of an input integer, where the
+    aliquot sum of a number n is defined as the sum of all
+    natural numbers less than n that divide n evenly. For
+    example, the aliquot sum of 15 is 1 + 3 + 5 = 9. This is
+    a simple O(n) implementation.
+    @param input_num: a positive integer whose aliquot sum is to be found
+    @return: the aliquot sum of input_num, if input_num is positive.
+    Otherwise, raise a ValueError
+    Wikipedia Explanation: https://en.wikipedia.org/wiki/Aliquot_sum
+    
+    >>> aliquot_sum(15)
+    9
+    >>> aliquot_sum(6)
+    6
+    >>> aliquot_sum(-1)
+    Traceback (most recent call last):
+      ...
+    ValueError: Input must be positive
+    >>> aliquot_sum(0)
+    Traceback (most recent call last):
+      ...
+    ValueError: Input must be positive
+    >>> aliquot_sum(1.6)
+    Traceback (most recent call last):
+      ...
+    ValueError: Input must be an integer
+    >>> aliquot_sum(12)
+    16
+    >>> aliquot_sum(1)
+    0
+    >>> aliquot_sum(19)
+    1
+    """
+    if not isinstance(input_num, int):
+        raise ValueError("Input must be an integer")
+    if input_num <= 0:
+        raise ValueError("Input must be positive")
+    return sum(divisor for divisor in range(1, input_num) if input_num % divisor == 0)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()