Mertens

Let $n \in \mathbb{Z}^+$. Define the Mertens function $$M(n)=\displaystyle\sum_{k=1}^n \mu(k),$$ where $\mu$ is the Möbius function.

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  Graph of $M$.

Videos

Möbius Function - Merten's function (4 September 2007)
Möbius Function - Merten's conjecture (4 September 2007)

References

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