[seqfan] How fast are A034090, A034091 growing?

[Neil Sloane]

Let f(n) = sigma(n)-n, the sum of the divisors d of n with d < n.
The n for which f(n) reaches a new record high, and the corresponding
values of f(n), are A034090 and A034091.

The question is, how fast are these growing?
Also their ratio seems close to 1, can that be made more precise?

I'm not hoping for anything rigorous.  I would be happy with a
statistician's estimate.

Best regards
Neil

Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com