Radius of convergence of $\sum a_n x^{n^2}$

Let $\sum a_n x^n$ be a power series with radius of convergence $R$.

What is the radius of convergence of $\sum a_n x^{n^2}$?

Can anyone help me here?

• Do you know the formula with $\limsup |a_n|^{1/n}$? Use it for the second series. The indices with zero coefficients can be ignored for the computations of $\limsup$ – user147263 Oct 26 '14 at 18:16

Hint: Let $b_k:=a_n$ if $k=n^2$ and $b_k:=0$ else.
• Well, I thought about the formula with $\limsup$, commented by @WeaponofChoice. – Berci Oct 26 '14 at 18:31