I was going to ask the same question. It seems the canonicalest choice would be elements z of Z[i] with Re(z) > 0 and Im(z) >= 0. But there's something arbitrary about this. But even more natural might be to define the sum of aliquot parts in something like Z[i] / z ~ iz. I would hope this object would retain some kind of useful algebraic structure, that would be related to the ring structure of Z[i] as Z+ is related to the group structure of Z. --Dan Gene wrote: << In the ring Z[i], the units (divisors of 1) are +1, -1, +i, -i. Thus if d is a divisor of 3+i, so are -d, id, -id. In taking the sum of divisors, how do you make a canonical choice among the associates of each divisor? If you take them all, the sum is zero. In the rational integers, one chooses the positive divisor.
Sometimes the brain has a mind of its own.