Clearly if $p$ is prime, the sequence $\frac{\phi(p)}{p} \rightarrow 1$. In general, however, if $s_n \in S \subseteq \mathbb{N}$, we are not even guaranteed of the existence of: $\displaystyle \lim_{n \to \infty} \frac{\phi(s_n)}{s_n}$.
My question is this: Does there exist an infinite sequence $S \subseteq \mathbb{N}$ such that $\displaystyle \lim_{n \to \infty} \frac{\phi(s_n)}{s_n}=1$ and at most finitely many $s_i$ are prime?
My intuition tells me no, but I'm not sure. Having the above limit exist for some sequence alone is quite a strong statement, so having it equal one and contain finitely many primes is pretty restrictive. Admittedly, that isn't an argument and I've been having trouble finding one. Any thoughts would be appreciated.
EDIT: It just occurred to me that if $s_i=p_i^2$ for prime $p_i$, then the above holds. Reformulating, is there such an $S$ with finitely many prime powers?