Chebyshev psi function

The Chebyshev $\psi$ function is $$\psi(x) = \displaystyle\sum_{p^k \leq x} \log p = \displaystyle\sum_{n \leq x} \Lambda(n),$$ where $\Lambda$ denotes the Mangoldt function.

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

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  Plot of $\psi$ 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