Chebyshev theta function

The Chebyshev $\vartheta$ function is $$\vartheta(x) = \displaystyle\sum_{p \leq x} \log p,$$ where $p \leq x$ denotes that $p$ is a prime number less than the real number $x$.

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  Plot of $\vartheta$ on $[0,50]$.

• Chebyshevthetaplotto100.png

  Plot of $\vartheta$ on $[0,100]$.

• Chebyshevthetaplotto1000.png

  Plot of $\vartheta$ on $[0,1000]$.

Number theory functions

Chebyshev $\vartheta$

Chebyshev $\psi$

Euler $\phi$

Greatest prime factor

Mangoldt

Mertens

Möbius

Liouville $\lambda$

Prime counting

Riemann-Siegel $Z$

Riemann zeta

Sum of divisors

Totient