# Difficult interpolation problem

Let:

$r(1) = \sum_{n=1}^{\infty} \frac{1}{n^n}$

$r(2) = \sum_{m=1}^{\infty} \sum_{n=1}^{\infty} \frac{1}{(mn)^{mn}}$

$r(3) =\sum_{l=1}^{\infty} \sum_{m=1}^{\infty} \sum_{n=1}^{\infty} \frac{1}{(lmn)^{lmn}}$

Find the most natural interpolation of $r(z)$ on the complex plane $\mathbb{C}$ given the above scheme.