DLMF:27.12.E3 (Q8087)

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DLMF:27.12.E3
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    π ( x ) = x - 1 - p j x x p j + r 2 ( - 1 ) r p j 1 < p j 2 < < p j r x x p j 1 p j 2 p j r , number-of-primes-less-pi 𝑥 𝑥 1 subscript subscript 𝑝 𝑗 𝑥 𝑥 subscript 𝑝 𝑗 subscript 𝑟 2 superscript 1 𝑟 subscript subscript 𝑝 subscript 𝑗 1 subscript 𝑝 subscript 𝑗 2 subscript 𝑝 subscript 𝑗 𝑟 𝑥 𝑥 subscript 𝑝 subscript 𝑗 1 subscript 𝑝 subscript 𝑗 2 subscript 𝑝 subscript 𝑗 𝑟 {\displaystyle{\displaystyle\pi\left(x\right)=\left\lfloor x\right\rfloor-1-% \sum_{p_{j}\leq\sqrt{x}}\left\lfloor\frac{x}{p_{j}}\right\rfloor+\sum_{r\geq 2% }(-1)^{r}\*\sum_{p_{j_{1}}<p_{j_{2}}<\cdots<p_{j_{r}}\leq\sqrt{x}}\left\lfloor% \frac{x}{p_{j_{1}}p_{j_{2}}\cdots p_{j_{r}}}\right\rfloor,}}
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    DLMF:27.12.E3
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