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

[Charles Greathouse]

I extended A070319. I would love to see a b-file for A068509.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Wed, Sep 12, 2012 at 3:09 PM, Max Alekseyev <maxale at gmail.com> wrote:
> William,
> Could please extend b-files for both sequences (say, to a thousand
> terms) so that they clearly indicate differences?
> Regards,
> Max
>
> On Tue, Sep 11, 2012 at 7:55 PM, William Rex Marshall
> <w.r.marshall at actrix.co.nz> wrote:
>> 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.