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