ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D4807
Möbius function
Formulation 0
The Möbius function is the D4948: Integer function \begin{equation} \mathbb{N} \to \{ -1, 0, 1 \}, \quad n \mapsto \begin{cases} (-1)^m, \quad & n \text{ equals a product of } m \text{ distinct prime integers} \\ 0, \quad & \text{otherwise} \end{cases} \end{equation}