29 Sep
2016
29 Sep
'16
2:28 p.m.
To my knowledge, this question is still entirely shrouded in mystery. There may have been advances I know not of, however. On Thu, Sep 29, 2016 at 3:11 PM, David Wilson <davidwwilson@comcast.net> wrote:
Let f(n) = sigma(n) - n = sum of proper divisors of n.
If you iterate f on positive integer n, some trajectories end at 0 (where you cannot continue, since 0 is not in the domain of f), some trajectories loop (e.g. 6 -> 6... or 220 -> 284 -> 220...). For other numbers, like 138, the trajectory seems to diverge.
Can we prove that there exist divergent trajectories?
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