Definition:Von Mangoldt Function

Definition

The von Mangoldt function $\Lambda: \N \to \R$ is defined as:

$\map \Lambda n = \begin {cases} \map \ln p & : \exists m \in \N, p \in \mathbb P: n = p^m \\ 0 & : \text {otherwise} \end {cases}$

where $\mathbb P$ is the set of all prime numbers.

This sequence is A014963 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Also known as

Some sources dispose of the von, and instead refer to the von Mangoldt function as just the Mangoldt function.

Also see

• Results about the von Mangoldt function can be found here.

Source of Name

This entry was named for Hans Carl Friedrich von Mangoldt.