[seqfan] Re: list of all non-prime coprimes of the full set of primorial numbers

Charles Greathouse charles.greathouse at case.edu
Tue Apr 25 22:56:25 CEST 2017

I think it would be reasonable to re-submit the clarified sequence.
Possible name: numbers n < P coprime to P for some primorial P. Question:
what is the asymptotic growth if this sequence? Clearly a(n) > kn for all k
and all large n.

On Fri, Apr 21, 2017 at 6:43 AM Jamie Morken <jmorken at shaw.ca> wrote:

> Hi,>The definition is not clear.  Note that  gcd(121,2310)=11, so why is
> >121 on the list?
> >Or, if 121 is on the list, why not 49?
> 121 is on the list as gcd(121,210)=1, the sequence includes all coprimes
> as long as they are coprime
> to at least one primorial x.  49 isn't on the list as I only included
> coprimes of primorials if they
> are smaller than the primorial.  49 isn't coprime to any primorial greater
> than Pn(3) = 30 so it isn't on
> the list.>Also, what is Pn? What is the difference between Pn(210) and 210
> ? >Did you mean to say >Pn(4) = 210 rather than Pn(210)? >Best regards
> >NeilYes thanks I meant to say Pn(4) = 210, where 210 is the fifth
> primorial, and Pn(0) = 1
> >Best regards
> >Neil
> reply to Franklin:
> >The full set of primorials is infinite, and only 1 is coprime to all of
> them. This is just the numbers coprime to 210, which is rather arbitrary.
> The values that are coprime to 210 also contains 253 which isn't in the
> list (see updated definition of coprimes smaller than Pn only included in
> the sequence).
> Should I resubmit the sequence if the definition is correct now?  Thanks.
> cheers,
> Jamie
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Charles Greathouse
Case Western Reserve University

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