liouville_lambda.py

"""
== 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)
frommaths.prime_factorsimportprime_factors


defliouville_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)
 1
 >>> 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
 """
ifnotisinstance(number, int):
msg=f"Input value of [number={number}] must be an integer"
raiseTypeError(msg)
ifnumber<1:
raiseValueError("Input must be a positive integer")
return-1iflen(prime_factors(number)) %2else1


if__name__=="__main__":
importdoctest

doctest.testmod()