Mangoldt
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The Mangoldt function is defined by the formula $$\Lambda(n) = \left\{ \begin{array}{ll} \log p, & n=p^k \mathrm{\hspace{2pt}for\hspace{2pt}some\hspace{2pt}prime\hspace{2pt}}p\mathrm{\hspace{2pt}and\hspace{2pt}integer\hspace{2pt}}k\geq 1, \\ 0, & \mathrm{otherwise}. \end{array} \right.$$
Graph of $\Lambda$.
Properties
Relationship between logarithm and Mangoldt
Videos
Number Theory 31: Liouville and mangoldt functions (8 January 2015)
Number theory: Arithmetic functions #1 (27 July 2012)
