convergence divergence - Interesting Power Series

The series is $\sum_{n=1}^{\infty} r(n)x^n$ , where $r(n)$ is defined as the divisor function. The question is , what is the radius of convergence of the power series?
Maybe it is not that interesting , but I am stuck with this one since we haven't had this function in our entire lecture and it came up in the latest worksheet.