# [seqfan] Re: Nomination for 250000.

Neil Sloane njasloane at gmail.com
Sat Nov 15 13:14:20 CET 2014

```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.
>
>
>

```