complex perfect numbers

[David Wasserman]

If a + bi divides z, then so do -b + ai, -a - bi, and b - ai.  b + ai usually doesn't, so it doesn't make sense to include it.

If we add up all of these divisors, we get 0.  We can get nontrivial results by adding up divisors in one quadrant, or in one half-plane.

I couldn't find a standard definition of "perfect" in the Gaussian integers, so I'm in favor of using any definition that 1) is somehow related to the usual definition in N, and 2) leads to an interesting sequence.  Just make sure you specify the definition. 

 - David

>I suppose that a complex perfect number z is the sum of its divisors. And are only complex numbers in the first quadrant considered -- along with only divisors in the first quadrant?
> Can anyone tell me whether, if a + bi  is a divisor, does one also use b + ai? Is there any generally agreed upon work in this area?