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In mathematics, the Landau–Ramanujan constant occurs in a number theory result stating that the number of positive integers less than x that are the sum of two square numbers, for large x, varies as

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

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 that are the sum of two squares, then

\( \lim_{x\rightarrow\infty} \frac{N(x)\sqrt{\ln(x)}}{x}\approx 0.76422365358922066299069873125. \)

External links

Weisstein, Eric W., "Landau–Ramanujan Constant", MathWorld.
(sequence A064533 in OEIS)

Mathematics Encyclopedia

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