[seqfan] Re: Destinies of sums of proper divisors.

[David Wilson]

I also wanted to make this observation on aliquot sequences:

Let s(n) be the sum of divisors of n, and f(n) = s(n)-n be the sum of 
aliquot divisors. We are discussing the trajectory of f(n).

Note that if n is a large number of the form 28k with k odd, then f(n) 
is likely to be a yet larger number of this form. If a sufficiently 
large number of this form occurs in the trajectory of n, the subsequent 
trajectory is likely retain that form and grow. Once it has grown 
sufficiently large, in the unlikely event it loses the form 28k, it is 
likely to recover that form after a few iterations a few iterations of 
and resume its growth.

For this reason, I conjecture that f(n) is very likely to include 
divergent trajectories, and that n = 276 is probably one of them.