In article <vznek.148507$Kb.127005@[EMAIL PROTECTED]
>, Jack
<jj@[EMAIL PROTECTED]
> wrote:
> Paul,
>
> >> It's
> >> writing out the definition of t: N ---> N is arbitrary, and my not
> >> knowing
> >> whether the change in definition of t(n) will mean that anything
needs to
> >> be
> >> said as regards c(n), which after the second definition is laid down
> >> becomes
> >> c(n,J).
> >
> > You can't do that; c and c(-,J) are two different things. What you
> > _can_ do is call your "count the divisors" function t_J and then
> > _define_ c(n, J) = c_(t_j)(n). In fact that wouldn't be a bad idea
> > since subscripted subscripts are to be avoided if possible.
>
>
> So after my first definition, in which t: N--->N is arbitrary, I write
'let
> c_t(n) = (1/2)*t(n)*(t(n) - 1)?
Fine. In fact, c_t _is_ your first definition. I still don't understand
your attachment for the redundant "arbitrary".
> Then I have my 'count the divisors' phase and I write 'let t_J(n) be the
> number of primes in J that divide n. And then I define c(n,J) as
> (1/2)*t_J(n)*(t_J(n) - 1)?
That would be OK.
I don't know what follows but I wonder about the necessity of your
first definition. Are you going to be looking at (1/2)*g(n)*(g(n) - 1)
where g is some function _other_ than a "count the divisors" function?
If not, skip the c_t definition.
> I suppose that means I have to redefine, similarly, all my terms that
depend
> upon t....?
Since I don't know what's coming, I can't comment.
--
Paul Sperry
Columbia, SC (USA)
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