A

a

```
package com.thealgorithms.maths;
/*
* Java program for liouville lambda function
* For any positive integer n, define λ(n) as the sum of the primitive nth roots of unity.
* It has values in {−1, 1} depending on the factorization of n into prime factors:
* λ(n) = +1 if n is a positive integer with an even number of prime factors.
* λ(n) = −1 if n is a positive integer with an odd number of prime factors.
* Wikipedia: https://en.wikipedia.org/wiki/Liouville_function
*
* Author: Akshay Dubey (https://github.com/itsAkshayDubey)
*
* */
public class LiouvilleLambdaFunction {
/**
* This method returns λ(n) of given number n
*
* @param number Integer value which λ(n) is to be calculated
* @return 1 when number has even number of prime factors
* -1 when number has odd number of prime factors
* @throws IllegalArgumentException when number is negative
*/
static int liouvilleLambda(int number) {
if (number <= 0) {
//throw exception when number is less than or is zero
throw new IllegalArgumentException(
"Number must be greater than zero."
);
}
//return 1 if size of prime factor list is even, -1 otherwise
return PrimeFactorization.pfactors(number).size() % 2 == 0 ? 1 : -1;
}
}
```