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Old 2009-03-20, 17:16   #2
R.D. Silverman
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Nov 2003

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Originally Posted by philmoore View Post
The aliquot sequence chasers might be doing it for the sheer fun of it, as they get to combine a number of different factoring techniques in pursuit of the extension of sequences. There are a number of unresolved conjectures in this area (see Richard Guy's book, for example) and Guy and Selfridge have conjectured that "most" sufficiently large even numbers generate aliquot sequences that do not terminate. Perhaps the data generated by these people can help formulate a reasonable conjecture of what "most" means.

It is clear, from a mathematical point of view what 'most' means:
a set of density 1. Unfortunately, no amount of computation will
ever resolve this conjecture. On the other hand, I have suggested projects
for which computation CAN resolve the conjecture.
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