Mangoldt

The Mangoldt function is defined by the formula $$\Lambda(n) = \left\{ \begin{array}{ll} \log p, & n=p^k \mathrm{\hspace{2pt}for\hspace{2pt}some\hspace{2pt}prime\hspace{2pt}}p\mathrm{\hspace{2pt}and\hspace{2pt}integer\hspace{2pt}}k\geq 1, \\ 0, & \mathrm{otherwise}. \end{array} \right.$$

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  Graph of $\Lambda$.

Properties

Relationship between logarithm and Mangoldt

Videos

Number Theory 31: Liouville and mangoldt functions
Number theory: Arithmetic functions #1

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