Infinite sum of prime-counting function The function, $\pi (n) $ is the number of prime number less than or equal to $n$.
So, my question is the radius of convergence about
$$\sum_{n = 0} ^ {\infty} {\frac {1}{\pi (n)} x^n } $$
What is radius of convergence in this power series?

Hint: $\pi(n)\sim {n\over \log{n}}$ and $\pi(n+1)\le \pi(n)+1$
