For an integer z,
$$ z = \epsilon \prod_i p_i^{k_i}, $$
where $\epsilon$ is and a unit and every $p_i$ is a Gaussian prime in the first quadrant then the sum of the Gaussian divisors is
$$ \sigma_1 (z) = \prod_i \frac{p_i^{k_i + 1} - 1}{p_i - 1} $$
For z = 5, the output is $4 + 8i$
How does this work for $z=5$? The sum of divisors should be $(1 + 2i) + (2 + i) = 3 + 3i$?
