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==Properties and applications==
The Möbius function is [[multiplicative function|multiplicative]] (i.e. μ(''ab'') = μ(''a'') μ(''b'') whenever ''a'' and ''b'' are [[coprime]]). The sum over all positive divisors of ''n'' of the Möbius function is zero except when ''n'' = 1:
:<math>\sum_{d | n} \mu(d) = \left\{\begin{matrix}1&\mbox{ if } n=1\\
0&\mbox{ if } n>1\end{matrix}\right.</math>
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