From: Christian.Radoux@skynet.be
Newsgroups: sci.math
Subject: Re: amicable tuples
Date: Sun, 12 Apr 1998 06:19:54 -0600

In article <3530422a.26480169@news.concentric.net>,
  bommel1@cris.com wrote:
>
> Hi all,
>
> besides the ordinary amicable numbers sigma_0(n)=m -- sigma(m)=n
> is there any knowledge about higher tuples? There are no triples <=
> 200,000 and quadrupels <= 60,000 as I made my computer telling me
> today. But that means almost nothing :(
> Is there a proof that no other tuples than the well known twins might
> exist? Similar to Fermat's Assumption??
>
> Any enlightening idea will be appreciated :)
>
>  \
>   |
> _\|/_
>  /|\   Bommel
>
> ===================
> Moskito - ergo summ!
>
Here are some examples :

Oder 4 generators
-----------------
28158165
81128632
174277820
209524210
330003580
498215416

Order 5 generator
-----------------
12496

Order 28 generator
------------------
14316

Of course, any element of a cycle being also a generator of the same cycle, I
have written only one of them...

With best regards !

e-mail : Christian.Radoux@skynet.be
URL : http://users.skynet.be/radoux
(when my provider works...)


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Newsgroups: sci.math
From: Deinst@world.std.com (David M Einstein)
Subject: Re: amicable tuples
Date: Sun, 12 Apr 1998 16:39:04 GMT

Bommel (bommel1@cris.com) wrote:
: On Sun, 12 Apr 1998 06:19:54 -0600, Christian.Radoux@skynet.be wrote:

: >In article <3530422a.26480169@news.concentric.net>,
: >  bommel1@cris.com wrote:
: >>
: >> Hi all,
: >>
: >> besides the ordinary amicable numbers sigma_0(n)=m -- sigma(m)=n
: >> is there any knowledge about higher tuples? There are no triples <=
: >> 200,000 and quadrupels <= 60,000 as I made my computer telling me
: >> today. But that means almost nothing :(
: >> Is there a proof that no other tuples than the well known twins might
: >> exist? Similar to Fermat's Assumption??
: >Here are some examples :
: >
: >Oder 4 generators
: >-----------------
: >28158165
: >81128632
: >174277820
: >209524210
: >330003580
: >498215416
: >
: >Order 5 generator
: >-----------------
: >12496
: >
: >Order 28 generator
: >------------------
: >14316
: >
: Thankx so much! :)
: It looks like there are no tripletts. Is there any proof of that? Can
: anybody suggest some book about the entire topic?

	There is a book "Perfect Amicable and Sociable Numbers" (or
something like that) by Song Yan, but if you have access to a library
you will probably do better to look up the papers referenced in either
UPINT, or
http://www.astro.virginia.edu/~eww6n/math/SociableNumbers.html
or
http://xraysgi.ims.uconn.edu:8080/amicable.html

(Achim Flammenkamp may have some stuff on his web page, but I forget where that is)


:  \
:   |
: _\|/_
:  /|\   Bommel

: ===================
: Moskito - ergo summ!
-- 
David M Einstein      | Lord, grant me the companionship of those who seek
                      | the truth, and protection from those who have found
                      | it.