[seqfan] Re: Unitary AP Generalized 2

[M. F. Hasler]

On Tue, Mar 12, 2019 at 5:41 AM <zbi74583_boat at yahoo.co.jp> wrote:

>     More generally  it is possible to describe as follows
>     Sigma(x) = Sigma(y) = f(x,y)
>     The easiest function of x,y is x+y. If f(x,y) is replaced by more
> complicated function, it will become an interesting AP like this
> http://list.seqfan.eu/pipermail/seqfan/2018-December/018780.html
>
> I had a look at that post and searched the numbers.
The post does not refer to any sequence, but I found the k=4 numbers in
sequences
A144949 <http://oeis.org/A144949>, A144950 <http://oeis.org/A144950>,
A144951 <http://oeis.org/A144951> you have submitted back in 2009.
None of these sequence have any cross-reference (not even among themselves).
Also, it appears that the { m, = } pairs (where A144949(i) = A144950 (i)
= A144951(i)) are a subsequence of
A006086 <http://oeis.org/A006086> Unitary harmonic numbers(Maybe it's easy
for you to confirm or give counter-example.)
In any case I think you should edit the sequences to add these cross
references and such a comment.

Maybe the k=6 numbers (from the Dec.2018 post) are also already in the
OEIS?
Can you double-check and add the cross-refs or comment and/or link to your
related SeqFan posts for further information?

Maybe some of the sequences you mentioned in yesterday's mail are also at
least partially in OEIS?

Well, I had a quick glance : the { m, = } pairs of those you list later
(with k = 5, m  = -7, etc)
seem to be equal to A002827 = Unitary perfect numbers
It looks obvious that members of that sequence are solutions to your
equation with x=y and r.h.s. = 2x, so all these terms are immediately
confirmed.
You might have mentioned this... Anyway, it looks that there's already a
certain mount of related information in OEIS. OK, I agree that these are
the less interesting special cases, and your results with x =/= y are maybe
(?) not yet in OEIS. This should be clarified.

Regards,
Maximilian