Möbius Function/Examples/6

Example of Möbius Function

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

Then:

$\map \mu 6 = 1$

$\ds 6$

$=$

$\ds 2 \times 3$

Prime Decomposition of $6$

$\ds \leadsto \ \ $

$\ds \map \mu 6$

$=$

$\ds \paren {-1}^2$

as $6$ has $2$ distinct prime divisors

$\ds $

$=$

$\ds 1$

$\blacksquare$

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