[seqfan] Re: Highly cototient numbers

[Alonso Del Arte]

Thank you very much, Tony, for that surprising coincidence.
http://www.research.att.com/~njas/sequences/plot2a?name1=A082917&name2=a100827&tform1=untransformed&tform2=untransformed&shift=0&radiop1=xy&drawpoints=true
shows
that there is a definite close relationship between the two sequences. What
I find so surprising is that A082917 depends on the addition of primes,
while A100827 depends on multiplication of primes and their powers (but
there is of course also subtraction involved--this certainly calls for
further pondering).

Al

On Tue, Mar 16, 2010 at 4:25 PM, T. D. Noe <noe at sspectra.com> wrote:

>
> Today I calculated 176 terms for this sequence, up to about 1.6 x 10^6.  I
> will submit the b-file today, along with one for A101373, which counts the
> number of solutions.
>
> It appears that this sequence eventually has the same terms as the
> Goldbach-related sequence A082917 (numbers n with property that n can be
> written in more ways as a sum of two odd primes than any smaller even
> number).  In fact, the last 69 highly cototient numbers match 69
> consecutive terms of A082917, which will have a b-file of terms up to 10^7
> soon.
>
> Tony
>
>
>
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