[seqfan] Re: ln(A003418(n)) seems to be nearly equal to n... why?

[franktaw at netscape.net]

Ouch. Bad enough to use ln instead of the preferred log - but both in 
the same formula?

Franklin T. Adams-Watters

-----Original Message-----
From: Charles Greathouse <charles.greathouse at case.edu>

> I noticed that ln(lcm(1..n)) -- that is, ln(A003418(n)) -- is close 
to n,
> sometimes larger than n, and sometimes smaller than n.  Is there some 
deep
> number theoretical reason for this?

Indeed.  From the sequence:

An assertion equivalent to the Riemann hypothesis is: | log(a(n)) - n
| < sqrt(n)*(ln(n))^2. - Lekraj Beedassy (blekraj(AT)yahoo.com), Aug
27 2006

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Mon, Sep 19, 2011 at 5:41 PM, g_m at mcraefamily.com
<g_m at mcraefamily.com> wrote:
> I noticed that ln(lcm(1..n)) -- that is, ln(A003418(n)) -- is close 
to n,
> sometimes larger than n, and sometimes smaller than n.  Is there some 
deep
> number theoretical reason for this?
>
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