[seqfan] Re: A046790, A046791 obscure, need clarification

[Neil Sloane]

Don, Vladimir,
thanks very much for those comments!  I will wait to see if there are any
further comments, and then I'll revise the two entries later today.
A046790 will get the "nice" label.

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.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com


On Mon, Jun 6, 2016 at 5:45 AM, Vladimir Shevelev <shevelev at bgu.ac.il>
wrote:

> If I am not missing anything, then
> A046790: Numbers n>=8 having a divisor k^2>=4
> such that n and n/k^2 are of the same parity.
> A046791: A046790(n)/(max k)^2, where k
> described in A046790.
>
>
> Best regards,
> Vladimir
>
>
> ________________________________________
> From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Neil Sloane [
> njasloane at gmail.com]
> Sent: 06 June 2016 00:03
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] A046790, A046791 obscure, need clarification
>
> Dear SeqFans, A046790 and A046791 from 1999 could use some clarification.
>
> It looks like they are a pair of sequences X(n) and Y(n) such that
> the arith. mean (X(n)+Y(n))/2 and the georm. mean
> sqrt(X(n)*Y(n)) are both integers.  But that does not explain where the
> numbers in A046790 come from. (There are many missing pairs, such as 4,4.)
>
> (There are 4 links to problems and solutions by Mohammad Azarian,
> which I tracked down on JSTOR.  But when I finally found all these links,
> they appear to have nothing to do with these sequences. Possibly
> these links should be deleted)
>
> A046790 has some comments that were added later that
> conjecture alternative definitions.
>
> But that doesn't help answer the question: what is the definition of
> A046790?
>
> Possibly it consists of numbers i such that there is a smaller number j
> such that (i+j)/2 and sqrt(i*j) are integers - could someone check if that
> is the case?
>
> 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.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
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