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Old 2011-04-22, 20:05   #6
Apr 2011
Baden, Germany

210 Posts

Originally Posted by Batalov View Post
Most tables don't bother with odd number sequences, but
you can generate your own simple table by
pari/gp> for (n=2,10000000,write("mytable1",n," ",sigma(n)-n))
and then analyze the output for cycles, multiple entries into a node etc...

After the sequence which ends with 6 was found, I played with this idea for a while. There are some bottlenecks in some descents, and some others are highly branched. Note: 28 is unreacheable (except from itself); it is a singleton. 6 and 496 have an entry and a cycle into itself... etc etc etc. Some highly branched nodes are
129     2731
127     2941
117     2971
116     2521
115     2311
115     2851
113     2881
111     2641
109     2761

...(there are undoubtedly nodes with more entries)...
This is similar to EndGame TableBases.

Incidentally, the OEIS sequence A048138 will describe the number of entries into a node n (offset of this sequence is 2).

For visualization, you may want to try something like Cytoscape.
thanks indeed. There is such a lot of input.
The Aliquot-pages to find the targets, the Pari/GP-function to find the sigma-lists, the OEIS-reference to check the nodes (wow, I never thought of nodes with such a lot of entries - hmm). It makes it much easier to finish the data for my prime family project.
I`ll try Cytoscape to visualize the results and will be back with some graphs - in due course ;-)
take care, cheers, Wini
Wini is offline   Reply With Quote