[seqfan] search for 15 consecutive numbers with exactly 12 divisors each

Max Alekseyev maxale at gmail.com
Fri Feb 4 22:17:51 CET 2022


It is my pleasure to communicate a message from an old friend Vladimir
Vladimir can read but not write to SeqFan (for some reason his messages are
bounced back).

I am looking for those who want to participate in the following distributed
computing project with the goal to find 15 consecutive numbers with exactly
12 divisors each.

Let M(k) be the maximum number of consecutive positive integers each having
exactly k divisors.
It is easy to see that M(k) = 1 for all odd k. When k is even, everything
becomes much more interesting.

To date, several hundred exact values of M(k) (for various k) are known.
But in all known cases we have M(k) <= 7.
Out of k's with M(k) > 7, it seems to be most realistic to find M(12), for
which we know bounds: 13 <= M(12) <= 15.
Since M(13), M(14),...M(23) are known, finding M(12) will allow us to add
12 new members to A119479.
More details can be found in a preprint https://arxiv.org/pdf/1811.05127.pdf

I have a code (in PARI) to search for a chain of 15 numbers, but an
estimate shows that on my computer it would take 7-10 years.
My hope is that if we pile on it collectively, we'd be able to accomplish
this task in a reasonable amount of time.

I am running multiple programs in PARI at once. Each uses one logical
processor core and quite a little bit of memory.
I manually restart all processes once every 5 days, so as not to waste time
(near 10 minutes) on restarting often.

Please contact me at val-etc at yandex.ru if you want to participate.
I will send the code and explanations.

Vladimir Letsko

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