[seqfan] Re: min(d(p^n-1)) for sufficiently large p
Max Alekseyev
maxale at gmail.com
Fri May 28 16:34:27 CEST 2010
On Fri, May 28, 2010 at 2:23 AM, <hv at crypt.org> wrote:
> franktaw at netscape.net wrote:
> :I think I would recommend something like "a(n) is the largest value m
> :such that p^n-1 has at least m divisors for sufficiently large primes
> :p", with a comment like "All terms in this sequence are conjectured;
> :even that such a value exists is a conjecture." You ought to be able to
> :find a suitable conjecture to support the values on-line somewhere -
> :perhaps at <http://www.primepuzzles.net/conjectures/>.
>
> Given the comments from Max and yourself, I think then it is better to
> fall back to the alternative approach - name the sequence by the formula
> and move the interpretation to a comment.
I support that. Your original %N sounded more like a property than a
definition (if it was taken as a definition, whole bunch of sequences
would satisfy it).
If you want to define the sequence that way, you'd probably need to do
so via algebraic properties of (factors of) the polynomial x^n - 1 and
its values on large primes (not just integers p^n - 1).
I also have a concern about "." symbol - does it mean multiplication?
If so, should more standard "*" be used instead?
Max
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