More possible multiplicative functions

[Mitchell Harris]

On Thu, 9 Jun 2005, Graeme McRae wrote:

>My understanding of "multiplicative" is incomplete, it seems.
>
>I thought a sequence was multiplicative if, for all coprime x and y,
>a(x)a(y)=a(xy).

That's the definition I've been going by, unqualified "multiplicative" is 
when coprime.

>Is there a different meaning for "completely" (or "fully") multiplicative?

"Completely multiplicative" is for when a(x)a(y) = a(xy) for -all- a,y, 
which implies that you can define the function on just primes, you don't 
have to define it for each prime power.

-- 
Mitch