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MathGroup Archive 2000

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Re: Divisors

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24353] Re: [mg24272] Divisors
  • From: Hans Havermann <hahaj at home.com>
  • Date: Sun, 9 Jul 2000 04:52:56 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

on 2000/7/7 1:19 AM, Andrzej Kozlowski wrote:

> I expect you do not really meant to say  that you want to construct a list
> containing possibly up to 2^40 elements. Maybe I am underestimating the
> speed of advance of computer technology, but I doubt that you will ever have
> enough Ram for such a job!

...<snip>...

> Note, however, that if you were really dealing with a number that factored
> into 40 different primes, than there would be 40!/(20!20!)= 137846528820
> divisors which themselves are products of 20 primes. That would still make a
> list which is far too large to fit into your RAM or indeed to be stored on
> any storage medium.

Thank you to all who responded to this. Yes, I'm aware now that some divisor
lists will never be gleaned in their entirety. You will find the proper
context for my original request at <http://members.home.net/hahaj/RSD.html>.
In effect, I'm trying to determine (therein) the "least solutions for
'difference between two squares is a repunit of length n'".

I believe I may have done so for repunits (10^n-1)/9, 1 < n < 197, with the
exception of n an element of {84, 90, 96, 108, 120, 126, 132, 140, 144, 150,
154, 156, 160, 162, 168, 180, 189, 192}, whose repunits have a large number
of divisors.

What I actually need to complete the sequences is *not* the entire list of
divisors for these repunits, but only (if it has 2k divisors) the k-th
divisor of the *sorted* divisor list. I don't know if it is possible to
generate this central divisor without first sorting the list of *all*
divisors.

Therein lies the rub. :)



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