Given parameters $a, b, c$; $max(a,b,c) \le 9000$. Your task is to compute $\sum\limits_{x = 1}^{a} \sum\limits_{y = 1}^{b} \sum\limits_{z = 1}^{c} d(x*y*z)$ by modulo $2^{30}$ where $d(n)$ is the divisor count function : the number of positive divisors of $n$.

This is the final problem in my recent OI Mocktest, I can only solve it to the first subtask: $max(a,b,c) \le 200$, by iterating over all triplets $(x,y,z)$ and adding $d(x*y*z)$ to the result variable, to compute $d(x*y*z)$, I used applied prime sieve.

Can you suggest the algorithm for the final subtask?

Any help would be highly appreciated!