[seqfan] Re: Strange comment in A003418
Max Alekseyev
maxale at gmail.com
Sun Oct 23 00:11:19 CEST 2011
I believe the source is http://arxiv.org/abs/math.NT/0008177
also published in Amer. Math. Monthly 109 (2002), 534--543
Max
On Sun, Oct 23, 2011 at 1:09 AM, Olivier Gerard
<olivier.gerard at gmail.com> wrote:
> Georgi,
>
> This kind of assertion is mostly meant as true for n large enough.
>
> More important, the commenter should have indicated a source (article, book,
> forum discussion)
> for his statement as there is a very extensive litterature on properties
> implying or depending on R.H.
> and equivalence with R.H. requires a proof.
>
> Anyway, in the form it is stated it is verified up to 2 < n < 3000 and the
> gap seems large enough, but one
> can have surprises when dealing with functions constructed from primes, the
> first
> counter-examples to very reasonable conjectures appearing well beyond the
> computational
> horizon of experimental mathematics (ex Skewes number).
>
> Regards,
>
> Olivier
>
>
> On Sat, Oct 22, 2011 at 12:31, Georgi Guninski <guninski at guninski.com>wrote:
>
>> A003418 a(0) = 1; for n >= 1, a(n) = least common multiple (or lcm) of {1,
>> 2, ..., n}
>>
>> An assertion equivalent to the Riemann hypothesis is: | log(a(n)) - n | <
>> sqrt(n) * log(n)^2. - Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 27 2006
>>
>
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