1. Given that by Möbius inversion formula we have that and since is multiplicative it follows that is multiplicative (if is multiplicative then so is )

Note also that (where the product runs through the prime divisors of n)

Thus:

2. Consider the Inclusion-exclusion principle - Wikipedia, the free encyclopedia

and calculate , and from there find the formula for and conclude that it's multiplicative

To calculate find the prime divisors of 2004, these are and thus: