I think there's hope in the case of the 34155 conjecture. There are powerful techniques available using sigma_{-1} which might be brought to bear. I feel like the 2e11 lower bound could be used to find a narrow range (2, 2.00...] in which sigma_{-1}(n) must reside, and then... well, I don't know or else I'd try to prove it myself. But in any case the odd digit problem looks much less amenable to solution. Charles Greathouse Analyst/Programmer Case Western Reserve University On Wed, Apr 18, 2012 at 12:17 PM, Hans Havermann <gladhobo@teksavvy.com> wrote:
James Buddenhagen:
Is this known to be a finite sequence?
I think the best we can ever really do with this sort of problem is conjecture it to be true and provide a large number up to which it is known to be true. There was another such question brought up recently on SeqFan asking if 34155 is the only odd number equal to the sum of its proper divisors greater than (or equal to) its square root.
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