algorithm: Liouville lambda function (#7986)

* feat: Add liouville lambda function

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* refactor: Refactor if-else block

* refactor: Refactor error handling for -ve numbers

* refactor: Remove # doctest: +NORMALIZE_WHITESPACE

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maths/liouville_lambda.py

@@ -0,0 +1,45 @@
+"""
+== Liouville Lambda Function ==
+The Liouville Lambda function, denoted by λ(n)
+and λ(n) is 1 if n is the product of an even number of prime numbers,
+and -1 if it is the product of an odd number of primes.
+
+https://en.wikipedia.org/wiki/Liouville_function
+"""
+
+# Author : Akshay Dubey (https://github.com/itsAkshayDubey)
+from maths.prime_factors import prime_factors
+
+
+def liouville_lambda(number: int) -> int:
+    """
+    This functions takes an integer number as input.
+    returns 1 if n has even number of prime factors and -1 otherwise.
+    >>> liouville_lambda(10)
+    1
+    >>> liouville_lambda(11)
+    -1
+    >>> liouville_lambda(0)
+    Traceback (most recent call last):
+        ...
+    ValueError: Input must be a positive integer
+    >>> liouville_lambda(-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: Input must be a positive integer
+    >>> liouville_lambda(11.0)
+    Traceback (most recent call last):
+        ...
+    TypeError: Input value of [number=11.0] must be an integer
+    """
+    if not isinstance(number, int):
+        raise TypeError(f"Input value of [number={number}] must be an integer")
+    if number < 1:
+        raise ValueError("Input must be a positive integer")
+    return -1 if len(prime_factors(number)) % 2 else 1
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()