multiplicatively problematic sequences

[Mitchell Harris]

In my search for possibly multiplicative sequences, a large number were 
found that are multiplicative for n >= 1, but somehow it doesn't seem 
right to call them multiplicative. For example, there are a large number 
of continued fractions of sqrt(n) that pass the test. See A010121 
(sqrt(7)), A010122 (sqrt(13)), etc. for examples. It just doesn't seem 
right somehow that these are multiplicative, yet, as functions, they 
definitely are. The cyclic nature of these functions helps, as does 
a(n) = 1 for n odd. 

Is it 'right' that these are multiplicative? They are defined for n=0, but 
that shouldn't deny their multiplicativity, should it? 

They are cyclic, which is in some sense..um.. boring but then so is, for 
example, A011582 Legendre(n,11) (cyclic, that is, not boring).

So, what do you think?

-- 
Mitch Harris