Number of different ways that a number can be represented as the sum of two square?

Question

Let $r(n)$ denote the number of different ways in which a natural number $n$ can be expressed as the sum of two squares. Is there any function $f(n)$ such that $r(n) \geq n^{f(n)}?$

Answer 1

No, because there are many $n$ for which $r(n)=0$ but $n^{f(n)} \gt 0$ for any real $f(n)$