Create MobiusFunction.py

Author: QuantumNovice

MobiusFunction.py

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+
+def is_square_free(factors):
+    '''
+    This functions takes a list of prime factors as input.
+    returns True if the factors are square free.
+    '''
+    for i in factors:
+        if factors.count(i) > 1:
+            return False
+    return True
+    
+
+def prime_factors(n):
+    '''
+    Returns prime factors of n as a list.
+    '''
+    i = 2
+    factors = []
+    while i * i <= n:
+        if n % i:
+            i += 1
+        else:
+            n //= i
+            factors.append(i)
+    if n > 1:
+        factors.append(n)
+    return factors
+
+def mobius_function(n):
+    '''
+    Defines Mobius function
+    '''
+    factors = prime_factors(n)
+    if is_square_free(factors):
+        if len(factors)%2 == 0:
+            return 1
+        elif len(factors)%2 != 0:
+            return -1
+    else:
+        return 0