Define $f(n) = |\{m : m\le n, \exists k \text{ s.t. }\phi(k) = m\}|$.

Clearly, $f(n)\le \left\lfloor \frac{n}{2}\right\rfloor + 1$ since $\phi(n)$ is even for all $n > 2$.

Is $\limsup_{n\rightarrow\infty} \frac{f(n)}{n} > 0$. It is less than $\frac{1}{2}$ by my previous statement, but I don't know how to proceed.