Category:Möbius Function

This category contains results about the Möbius function.
Definitions specific to this category can be found in Definitions/Möbius Function.

Let $n \in \Z_{>0}$, that is, a strictly positive integer.

The Möbius function is the function $\mu: \Z_{>0} \to \Z_{>0}$ defined as:

$\map \mu n = \begin{cases} 1 & : n = 1 \\ 0 & : \exists p \in \mathbb P: p^2 \divides n\\ \paren {-1}^k & : n = p_1 p_2 \ldots p_k: p_i \in \mathbb P \end{cases}$