[seqfan] Re: Is A070319 the same as A068509?

[Max Alekseyev]

It is clear that A070319(n) <= A068509(n).
But they are different even asymptotically: A068509(n) = O(sqrt(n))
while A070319(n) does not have polynomial growth.
I did not check what is smallest n for which they are different but
n=625 gives a counterexample:

A070319(625) = 24 < A068509(625).

The inequality here is implied by the set {1, 2, ..., 25} where each
pair of elements has l.c.m. <= 625.

Regards,
Max

On Mon, Sep 10, 2012 at 3:06 AM, David Scambler <dscambler at bmm.com> wrote:
> http://oeis.org/A068509
> A070319 Max( tau(k) : k=1,2,3,...,n ) where tau(n)=A000005(n) is the number of divisors of x.
> 1, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8,
>
> http://oeis.org/A070319
> A068509 a(n) = maximum length of a subset in {1,..,n} whose integers have pairwise l.c.m. not exceeding n.
> 1, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8,
>
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