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

[William Rex Marshall]

On 11/09/2012 5:25 p.m., Max Alekseyev wrote:
> 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:

The two sequences first differ when n = 336, due to the set of 21 
elements {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 21, 24, 30, 
36, 42, 48} where each pair of elements has lcm <= 336, while no 
positive integer <= 336 has more than 20 divisors. Therefore 
A068509(336) = 21 and A070319(336) = 20.