[seqfan] Re: Strange comment in A003418

[Olivier Gerard]

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
>