The Möbius function

3.The properties of The Möbius function

Property 3.1

Let is multiplicative function then the following formula is appropriate

Property 3.2 Special case

The sum of the Möbius function over all positive divisors of n (including n itself and 1) is zero except when 



Proof.



now let , then and ;

If , . So there are in

for all of d

Because

, ,

So, for