Möbius Function/Examples/2

Example of Möbius Function

For $n \in \Z_{>0}$, let $\map \mu n$ denote the Möbius function of $n$.

Then:

$\map \mu 2 = -1$

$\ds 2$

$=$

$\ds 2^1$

Note that $2$ is prime

$\ds \leadsto \ \ $

$\ds \map \mu 2$

$=$

$\ds \paren {-1}^1$

Definition of Möbius Function

$\ds $

$=$

$\ds -1$

$\blacksquare$

2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Möbius function