[seqfan] Re: Need help with interesting sequences suggested by Feb 2021 Monthly

[Hugo Pfoertner]

To have a landing point, I quickly created a PARI program that maps the
positions of the quotients phi(m^2) / phi (n^2) back to A038568 / A038569,
with m and n taken in the order of the two sequences.

The result is in https://oeis.org/draft/A340922

Hugo

On Fri, Feb 19, 2021 at 3:02 AM Neil Sloane <njasloane at gmail.com> wrote:

> The article
> Hongjian Li , Pingzhi Yuan & Hairong Bai (2021) Positive Rational Numbers
> of the Form φ( m^2 ) / φ( n^2 ) , American Mathematical Monthly, 128:2,
> 174-176, DOI: 10.1080/00029890.2021.1850142
>
> shows that for every positive rational number there corresponds a unique
> pair of integers (m,n) satisfying certain properties.  They only give one
> example.
>
> It might be interesting to apply their procedure to the standard  list of
> rational numbers arranged in the order
>
> 1/1, 1/2, 2/1, 1/3, 3/1, 2/3, 3/2, 1/4, 4/1, 3/4, 4/3, ... (this is A038568
> <https://oeis.org/A038568>/A038569 <https://oeis.org/A038569>).
>
> Look at the m values and the n values that are obtained. Two potential
> sequences for the OEIS!
>
> If anyone needs a copy of the article let me know.
>
> 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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