Paul,
>
> First, are you familiar with Legendre's identity?
Not until now.
Let P be a product of
> distinct primes (like your a(m)) and let A be a set of integers ( like
> your [x, y] ). Lengendre's identity is a formula (sort of) for the
> number of integers in A which share _no_ primes with P. It seems to me
> that your o(x,y,m) is exactly y - x + 1 minus that number.
>
Yes, it appears so.
> The reason for my M(J,C) instead of your M_1 is that it is frequently
> better to start with a general definition and then specialize (kind of
> like C+ programming).
> Using 0's and 1's has the advantage of letting you use logical
> operations; for instance if you OR the columns of M(P,C) the result
> will have 1's in exactly the rows corresponding to primes which divide
> at least one of the elements of C.
Ah, but I really need to know the precise wording I should use. So far my
best guess is "We shall be constructing arrays comprising entries of ones
and zeroes, in which the first column, containing exclusively ones, is
indexed by zero."
> Your paragraph quoted above is a little too vague for me to be of any
> help. Are you going to change m's or intervals or both or none of the
> above. How many changes at one time are you going to want to make?
>
Generally my argument takes the pattern: "For any given m, and for all
intervals of length y-x+1..."
Apart from concluding that o(x,y,m) changes, in general I only want to
change one other variable out of those that I cited earlier in this
thread,
but this change is prescribed for an unspecified number of n over [x,y].
It
requires of me to introduce the set R(n), mentioned in the first thread I
posted to this NG.
With thanks.
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