Number of representable as sum of 2 squares How to find asymptotically (or some reasonable bound, at least $ o(n) $) number of numbers, representable as a sum of squares of 2 numbers? (in case of bound I am interested in both: lower and upper bounds)
I know how to find explicitly the number of ways to represent given number in such a way. (can be found here)
Thank you!
P.S. For one lower bound you can use this problem, it'll give you somewhat $ \Omega (n^{\frac{3}{4}}) $.

Let $S_2(x)$ be the number of integers $\leq x$ which are a sum of two squares. Landau, in 1906, showed that
$$S_2(x) \sim K \frac{x}{\sqrt{\log x}}$$
where 
$$K = \frac{1}{\sqrt{2}} \prod_{p \equiv 3 \mod 4} \frac{1}{\sqrt{1-p^{-2}}}$$
I can't find a proof online, but there are references to the statement in many places, such as here.
