$x/\{sqrt\{ln(x)\}\}.$

The constant of proportionality is the Landau–Ramanujan constant, which was discovered independently by Edmund Landau and Srinivasa Ramanujan.

More formally, if N(x) is the number of positive integers less than x which are the sum of two squares, then

$lim\_\{xrightarrowinfty\}\; frac\{N(x)sqrt\{ln(x)\}\}\{x\}approx\; 0.76422365358922066299069873125.$

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