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"""

== 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)

>>> 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):

msg = f"Input value of [number={number}] must be an integer"

raise TypeError(msg)

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()

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