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

[Vladimir Shevelev]

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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