Added Mobius Function (#1058)

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Author: QuantumNovice

maths/is_square_free.py

@@ -0,0 +1,39 @@
+"""
+References: wikipedia:square free number
+python/black : True
+flake8 : True
+"""
+from typing import List
+
+
+def is_square_free(factors: List[int]) -> bool:
+    """
+    # doctest: +NORMALIZE_WHITESPACE
+    This functions takes a list of prime factors as input.
+    returns True if the factors are square free.
+    >>> is_square_free([1, 1, 2, 3, 4])
+    False
+    
+    These are wrong but should return some value
+    it simply checks for repition in the numbers.
+    >>> is_square_free([1, 3, 4, 'sd', 0.0])
+    True
+    
+    >>> is_square_free([1, 0.5, 2, 0.0])
+    True
+    >>> is_square_free([1, 2, 2, 5])
+    False
+    >>> is_square_free('asd')
+    True
+    >>> is_square_free(24)
+    Traceback (most recent call last):
+        ...
+    TypeError: 'int' object is not iterable
+    """
+    return len(set(factors)) == len(factors)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

maths/mobius_function.py

@@ -0,0 +1,43 @@
+"""
+Refrences: https://en.wikipedia.org/wiki/M%C3%B6bius_function
+References: wikipedia:square free number
+python/black : True
+flake8 : True
+"""
+
+from maths.prime_factors import prime_factors
+from maths.is_square_free import is_square_free
+
+
+def mobius(n: int) -> int:
+    """
+    Mobius function
+    >>> mobius(24)
+    0
+    >>> mobius(-1)
+    1
+    >>> mobius('asd')
+    Traceback (most recent call last):
+        ...
+    TypeError: '<=' not supported between instances of 'int' and 'str'
+    >>> mobius(10**400)
+    0
+    >>> mobius(10**-400)
+    1
+    >>> mobius(-1424)
+    1
+    >>> mobius([1, '2', 2.0])
+    Traceback (most recent call last):
+        ...
+    TypeError: '<=' not supported between instances of 'int' and 'list'
+    """
+    factors = prime_factors(n)
+    if is_square_free(factors):
+        return -1 if len(factors) % 2 else 1
+    return 0
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()