> I still think it is a mistake to have the exceptional first column. If
> you really, really need it you could do something like
> "Let p(2) < ... < p(m + 1) be the first m primes and let p(1) = 1. Let
> x = x(1) < ... < x(n) = y (or x(n) = x + a - see below) be consecutive
> integers. Let M_1 be the m + 1 by n matrix (m(i,j)) where m(i,j) = 1 if
> p(i) divides x(j) and m(i,j) = 0 otherwise."
I'm afraid don't understand. The columns in M_(1) in which I want there
to
be m entries are the columns indexed by zero and multiples of a. I don't
see
how your expressions above say this.
Incidentally, how would I express the sum of all the entries, of value
1,
in the n-th column, for an array in which the number of such entries in a
column is not determined by divisibility? Following my definition "Given
an
interval [x,y] of integers, define N(x,y,m) to be the sum of t(n,m) for n
in
[x,y]", I had originally imagined it might be (in TeX) "\sum N(n)"; but we
are back to the same problem: N pertains to the matrix M_1, but I am
thinking of an array. How might I re-jig my definitions and/or mode of
notation?
With thanks.
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