We know by the prime number theorem that $\lim_{n\to\infty}\frac{\pi(n)}{n\,/\ln n} = 1$ An even better approximation is $\lim_{n\to\infty}\frac{\pi(n)}{\int_2^n\frac{1}{\ln t}\mathrm{d}t} = 1$.
Is there a similar formula that approximates the distribution of natural numbers of the form $p^n$ where $p$ is a prime? That is, an approximation of $$\pi'(x)=\left|\,\Pi'\cap\{1,\ldots,x\}\,\right| \qquad\mbox{ where }\quad \Pi'=\{p^n\;|\;p\mbox{ is prime}, n\in\mathbb{N}\}$$
(There is already a question that asks if $\lim_{n\to\infty}\frac{\pi'(n)}{n}=0$, but I'm interested in a more precise approximation.)