20141119, 22:54  #12 
"Ed Hall"
Dec 2009
Adirondack Mtns
3^{3}×7×17 Posts 
Thanks. I had considered trying to construct some cycles per the described manner, but decided those constructable would have been, to any limit I might easily pursue. Now seeding, I hadn't considered. I may look more into that...

20141122, 04:07  #13  
"Ed Hall"
Dec 2009
Adirondack Mtns
3^{3}·7·17 Posts 
Quote:


20141122, 04:38  #14  
"Phil"
Sep 2002
Tracktown, U.S.A.
1,117 Posts 
Quote:
Do there exist sociable numbers of order three? They must be rare, as none have ever been found. 

20141122, 10:49  #15  
"Frank <^>"
Dec 2004
CDP Janesville
2×1,061 Posts 
Quote:
In fact, in the wrapup for the section on the 3cycle rule, he said that finding a 3cycle is likely to be as hard as finding an oddprefect number, in his opoinion. 

20141122, 16:11  #16 
"Ed Hall"
Dec 2009
Adirondack Mtns
C8D_{16} Posts 
Thanks. Although I'm limiting my search to 4cycle (except for the one machine recently changed), they will record any three cycles, if one happens along.

20141123, 18:15  #17 
Nov 2011
Saint Maur, France
2·5^{2} Posts 
Ed, Congrats for your 4cycle.

20141124, 04:53  #18 
"Ed Hall"
Dec 2009
Adirondack Mtns
3^{3}×7×17 Posts 
Thanks Michel!

20141124, 15:02  #19 
"Ed Hall"
Dec 2009
Adirondack Mtns
6215_{8} Posts 
Wow, another one, already...
I restarted this project in May, after probably a year on and off of previous searching with no success up until recently, and now in less than a week of each other, two have appeared. Odds, anyone?
Code:
16687836720184 = 2^3 * 7 * 79 * 3772114991 19524467203016 = 2^3 * 23 * 439 * 2621 * 92221 18777616502584 = 2^3 * 23 * 113 * 3373 * 267749 18297447537416 = 2^3 * 71 * 179 * 179965453 Thanks to all who have assisted me in my endeavors... 
20141125, 17:38  #20 
Nov 2011
Saint Maur, France
32_{16} Posts 
Well done! I can imagine your thrill.

20141125, 17:54  #21 
Nov 2011
Saint Maur, France
62_{8} Posts 
Side notes.
djm.cc/sociable.txt: If you look closely at group 44, you'll see it is still the only group with powers of 2 that are all different; noticed by JM Pedersen when I wrote to him. OEIS: There are a few sequences related to 4sociable groups, you can see them by searching for A090615. Cheers. 
20141126, 04:34  #22  
"Ed Hall"
Dec 2009
Adirondack Mtns
3^{3}·7·17 Posts 
Quote:
Am I confusing something or did you mean powers of 3? I see they are 5 4 2 3. That is interesting. Thanks also for the OEIS link as well. 

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