[seqfan] Re: How fast are A034090, A034091 growing?

[Neil Sloane]

Hugo,  about the ratio of those two sequences, all I did was use the Plot 2
button (at the bottom of any OEIS page), to plot A034090 vs A034091, and
the result is astonishingly close to a dead straight tine (with wobbles). I
guess the slope isn't 1, maybe it will turn out to be something like log
log n.

Best regards
Neil

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



On Sun, Jan 15, 2023 at 1:45 PM <hv at crypt.org> wrote:

> I don't have answers, but the ratio seems the more likely to have been
> studied in the past.
>
> :Also their ratio seems close to 1, can that be made more precise?
>
> Not sure what you mean here - the last values in the b-files give a ratio
> around 5.35, and that will continue to grow.
>
> This is probably just random, but I note that if we call the ratio r_i,
> then the r_2750'th root of A034090(2750) is close to r_2750#.
>
> (1034758594602532800 ^ (1 / 5.3525611989641) ~= 2320.85710246872)
>
> Hugo
>
> Neil Sloane <njasloane at gmail.com> wrote:
> :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.
>
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