Cyclotomic polynomials and Mobius inversion

I am trying to prove the following facts about cyclotomic polynomials

$i) \Phi_n(1)=p \;\; if \;\; n=p^k , k \in \mathbb{Z}^{+}$

ii) $\Phi_n(1)=1$ if n is divisible by two or more primes

i understand the identity $n = \prod_{d|n,d\neq1}^{\;} \Phi_d(1)$ and how to derive it, but I am not sure how to apply Mobius inversion. What is $F$? What is $f$? Do n and d become 1?