von Mangoldt function

The von Mangoldt function, denoted by an upper-case lambda \( \Lambda (n) \), is an arithmetic function that plays a critical role in the distribution of primes.

\( \Lambda (n) = \begin{cases} \log p & \text{if }n=p^m \text{ for some prime } p \text{ and integer } m \ge 1, \\ 0 & \text{otherwise.} \end{cases} \)