Sorry It should be:
How can i show that
here are mobius function and Euler's phi function.
Remember that both, and are multiplicative, hence is multiplicative.
Now, recall the fact that if is a multiplicative arithmetic function then so is
From now on I will denote:
Now let's compute where is a prime number ( and s is greater than 0):
Now suppose is the prime descomposition of n.
Then
Now recall the fact that: and we are done