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Old 2009-03-20, 19:04   #4
R.D. Silverman
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Nov 2003

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Originally Posted by philmoore View Post
My question was how fast this density approaches 1 as N increases, for which I am not aware of any conjectures supported by data.

Ah. You are looking for a counting function.

#{s < n | aliquot(s) converges)

This would be very difficult to ascertain; It is likely to be something
that is at least as slow as loglog n. I don't know if the necessary
techniques are known to even approach this question theoretically.
It might yield to ergodic methods; ask Terry Tao.
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