Mangoldt Function

Definition

$\forall n \in \mathbb{Z},n \ge 1$ we define

\Lambda(n) = \ \left\{ \begin{array}{cl} \log p & \text{if } n=p^m \text{ for some prime }p \text{ and some }m\ge1,\\ 0 & : \text{otherwise} \end{array} \right.

Here is a table of values for the Mangoldt function:

$n:$	1	2	3	4	5	6	7	8	9	10
$\Lambda(n):$	0	$\log 2$	$\log 3$	$\log 2$	$\log 5$	0	$\log 7$	$\log 2$	$\log 3$	0