the Mobius function

hv at hv at
Wed Dec 15 19:54:08 CET 2004

Emeric Deutsch <deutsch at> 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

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