# von Mangoldt function

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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.

## Definition

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

**Cite as:**von Mangoldt function.

*Brilliant.org*. Retrieved from https://brilliant.org/wiki/von-mangoldt-function/