# Landau-Ramanujan Constant

Let $N$ be a natural number. Consider the equation

 $x^{2}+y^{2}=N$

Let $L(N)$ denote the number of naturals $z\leq N$ such that the equation $x^{2}+y^{2}=z$ has at least one integer solution $(x,y)$. The Laudau-Ramanujan constant is defined as the limit

 $\lim_{N\rightarrow\infty}\frac{L(N)\sqrt{\log(N)}}{N}\approx 0.764223653589220% 66299069873125$
Title Landau-Ramanujan Constant LandauRamanujanConstant 2014-03-06 12:39:16 2014-03-06 12:39:16 Filipe (28191) Filipe (28191) 2 Filipe (28191) Definition