[seqfan] Re: A Gaussian-integer analog of the sum-of-divisors function

[M. F. Hasler]

On Wed, Apr 27, 2022, 07:30 Neil Fernandez <primeness at borve.org> wrote:

> Hi Allan,
>
> I'm not sure whether I'm applying your rules correctly, but I get
> different values for a(8) and a(10):
>
> a(8):
>
> divisors in first octant or eighth (allowing both boundaries, not
> allowing 8 itself):
> {1, 1+i, 2, 2+2i, 4, 4+4i, 8, 1-i, 2-2i, 4-4i};
>

Maybe I get something wrong, but the last three are related to earlier ones
by a unit ( -i ) and so I would have thought they shouldn't be counted a
second time.

- M.

 Allan Wechsler <acwacw at gmail.com> writes
>

> >I have a draft at A353151 for a sequence that is intended to be an analog
> >of A000205, the sum of the divisors of n.
> >
> >This endeavor is a little bit fraught because every Gaussian divisor of n
> >is one of a set of four "associate" divisors, which are related by a
> >factors of a Gaussian unit. When we add up the divisors, we only want one
> >of each associated set; which one shall we choose?
> >
> >My choice was to add up the divisors that are the products of powers of
> >"positivish" Gaussian primes. "Positivish" means that the real part is
> >positive, and the imaginary part doesn't exceed the real part.
>