[seqfan] Re: Periodic structure in "integer log" A001414

[Allan Wechsler]

Another feature that is visible in Hans's detailed plot is an accumulation
in the vicinity (I think) of sqrt(n). Yet another is the striking "fan" in
the vicinity of (38000,1000).

It strikes me that we might get some insight by looking at this plot
restricted to 3-smooth numbers, 5-smooth numbers, and so on.

On Sun, Oct 11, 2015 at 4:22 PM, Frank Adams-Watters <franktaw at netscape.net>
wrote:

> As a start, note that the bottom of the graph contains only numbers with
> only small prime divisors; mostly 3 near the very bottom (since 3 is the
> where the maximum of log(n)/n occurs for integer n).
>
> It looks like there's a point where the graph goes abruptly from dense to
> this pattern - a particular value of a(n)/log(n) - but that could be an
> artifact of the graphics.
>
> Franklin T. Adams-Watters
>
> -----Original Message-----
> From: Allan Wechsler <acwacw at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Sun, Oct 11, 2015 8:03 am
> Subject: [seqfan] Periodic structure in "integer log" A001414
>
>
> Look at the graph of A001414. At the lower edge of the logarithmic
> scatterplot
> there is a set of fuzzy but unmistakable diagonal fringes,
> sloping toward the
> southeast. Their spacing gradually increases, and their
> slopes gradually
> decrease; they are more distinct toward the lower edge of
> the range. Is any
> explanation known?
>
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