Quote:
Originally Posted by Batalov
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
Code:
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.

Hey,
thanks indeed. There is such a lot of input.
The Aliquotpages to find the targets, the Pari/GPfunction to find the sigmalists, the OEISreference 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