[seqfan] Re: Integers split into 2 classes, and a "dark horse" sequence

[Peter Munn]

On Sat, March 30, 2019 5:54 am, Marc LeBrun wrote:
>>= Peter Munn <techsubs at pearceneptune.co.uk> wrote:
>> ...my current fascination with A059897 tempts me to view it as a
>> possible "dark horse"...
>
> Peter, glad you're enjoying this table!  The connection with the
> Fermi-Dirac sequence is nice.  Also (as Antti Karttunen notes) you can
> combine it with the (squares of) A059895 to recover the regular
> multiplication table.

Indeed.

In that respect, I seem to be getting somewhere towards proving that the
abelian group defined by A059897 on the positive integers is the only one
with (1) all elements self-inverse and (2) the result of the group
operation on k_1 and k_2 always being (using standard integer
multiplication) a divisor of k_1 * k_2. Perhaps someone whose group theory
is stronger and less rusty than mine can affirm this.

Peter