# the Mobius function

Alonso Del Arte alonso.delarte at gmail.com
Wed Dec 15 22:26:28 CET 2004

```Mathematica yields 0 for mu(0), MoebiusMu[0]. For a negative number n,
it yields the same value as |n|.

Is there a common or famous implementation of the Möbius
function? (Like the famous recursion implementation of factorials,
where 0! = 1).

Alonso

On Wed, 15 Dec 2004 18:54:08 +0000, hv at crypt.org <hv at crypt.org> wrote:
> Emeric Deutsch <deutsch at duke.poly.edu> wrote:
> :As far as I know, the Mobius function (mu) is defined only for
> :positive integers.
> :Is there a natural or customary assignment for n=0 ?
> :Maple yields mu(0)=-1.
>
> I don't think there is any natural extension to 0, except maybe mu(0) = 0:
> in general, I wouldn't expect any multiplicative function to have a natural
> extension to 0.
>
> mu(0) = 0 can be justified (sort of) by saying that it is divides any prime
> more than once (in fact an infinite number of times). But I can't offhand
> think of a way to make the extension relevant.
>
> Hugo van der Sanden
>

```