Lengths Of Runs In The #-Of-Divisors Sequence

[Joshua Zucker]

On 7/17/07, Leroy Quet <qq-quet at mindspring.com> wrote:
> I have recently submitted these sequences, which have already appeared in
> the database.

Should be easy to extend -- is it easier to post here first, asking
someone with a computer to extend them for you, and then submit enough
terms to begin with?

> It seems VERY likely to me that there is no infinite string of 1's, or of
> anything else, in sequence A131789 (ie. the terms of A131790 are all
> finite).
>
> Can it be PROVED that all terms of A131790 are finite, possibly using
> Hardy and Wright or some other such reference?

No need for Hardy and Wright, just Euclid -- there are infinitely many
primes.  Plus there are not any consecutive primes after 2.  Hence the
primes (2s) partition the list into finite chunks.

--Joshua Zucker