# [seqfan] Re: Nomination for 250000.

Max Alekseyev maxale at gmail.com
Sat Nov 15 16:30:02 CET 2014

```2^359-1, 2^397-1, 2^419-1 are all squarefree, which can be easily verified
with http://factordb.com

Regards,
Max

On Sat, Nov 15, 2014 at 7:14 AM, Neil Sloane <njasloane at gmail.com> wrote:

> Postscript: Juri, you said:
>
> Primes p such that 2^p - 1 is not squarefree: 359, 397, 419, ...
> (infinite).
>
> However, look at A237043:
> %S 6,20,21,110,136,155,253,364,602,657,812,889,979
>
> %N Numbers n such that 2^n - 1 is not squarefree, but 2^d - 1 is squarefree
> for every proper divisor d of n.
>
> Your sequence should be equal to the primes in A237043,
> but it is not.
>
> One of these two sequences must be wrong!
>
> Maybe someone could extend A237043 and even supply a b-file. A049094 also
> needs a b-file.
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Email: njasloane at gmail.com
>
>
> On Sat, Nov 15, 2014 at 6:51 AM, Neil Sloane <njasloane at gmail.com> wrote:
>
> > Dear Juri,
> > Please submit these two sequences to the OEIS,
> > and tell me the A-numbers:
> >
> > "Numbers n such that n, 2^n - 1 and binomial coefficient(2^n - 1, n) are
> > all squarefree: 1, 2, 3, 11, 29, 31, 51, 55, 57, ... (finite)
> >
> > Primes p such that 2^p - 1 is not squarefree: 359, 397, 419, ...
> > (infinite). "
> >
> > By the way, the second one should have a cross-reference
> > saying "These are the primes in A049094."
> >
> > Thank you
> >
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Email: njasloane at gmail.com
> >
> >
> > On Fri, Nov 14, 2014 at 5:51 PM, юрий герасимов <2stepan at rambler.ru>
> > wrote:
> >
> >>
> >> Numbers n such that n, 2^n - 1 and binomial coefficient(2^n - 1, n) are
> >> all squarefree: 1, 2, 3, 11, 29, 31, 51, 55, 57, ... (finite)
> >> or Primes p such that 2^p - 1 is not squarefree: 359, 397, 419, ...
> >> (infinite). JSG.
> >
> >
> >
>
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>

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