In article <4Yrek.246331$Ek2.105974@[EMAIL PROTECTED]
>, Jack
<jj@[EMAIL PROTECTED]
> wrote:
> Paul,
>
> > 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.
>
> If g represents arbitrary N--->N, then yes, I will need it.
Ah, but it's _not_ arbitrary - I qualified it.
> >
> >> 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.
> >
>
> Well, I've got, for example, N(x,y), which is the sum of t(n) -- or,
later,
> t_J(n) --
You mean t = t_J is a particular case. You should probably "tag" with
"t": like N(x, y, t).
> in a given interval [x,y];
_over_ [x, y]. (If you still have all intervals of the same length, you
would be doing everybody a favor if you dropped the redundant "y".)
> and indeed about 4 others that are
> sum_t(n) in such-and-such a set
Why the subscript? Is "t" the subscript or is it "t(n)"? Do you mean
t(n) is something other than an integer? That is t : |N -> |N is no
longer true? If so, you _do_ have problems.
> for values of such-and-such n in [x,y], and
> so on. That's what has worried me all along.
Merely a guess but you could probably just let S be a subset of [x, y]
and talk about sum(t(n) : n in S); "t" can be t_J or some other
function (provided its values can, in fact, be added). If you want to
give such sums a name you should "tag" the name with both "t" and "S".
Your N(x, y) would seem to be a special case with S = [x, y]. For me to
be of any real help I would need to see what leads up to this.
--
Paul Sperry
Columbia, SC (USA)
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