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mobius_function.py

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"""

References: https://en.wikipedia.org/wiki/M%C3%B6bius_function

References: wikipedia:square free number

python/black : True

flake8 : True

"""

from maths.is_square_free import is_square_free

from maths.prime_factors import prime_factors

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()