Compute sum of divisor count function for triplets of positive integers

Revision en7, by ace-in-the-hole, 2020-11-27 13:16:50

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!

#### History

Revisions

Rev. Lang. By When Δ Comment
en7 ace-in-the-hole 2020-11-27 13:16:50 19 Tiny change: '(x*y*z) $where$ ' -> '(x*y*z) $by modulo$2^30$where$ '
en6 ace-in-the-hole 2020-11-27 12:26:53 18 Reverted to en4
en5 ace-in-the-hole 2020-11-27 12:25:56 18
en4 ace-in-the-hole 2020-11-27 12:21:45 48
en3 ace-in-the-hole 2020-11-27 12:17:34 66
en2 ace-in-the-hole 2020-11-27 12:16:05 331 Tiny change: 'z)$, I use applied p' -> 'z)$, I used applied p' (published)
en1 ace-in-the-hole 2020-11-27 12:12:49 236 Initial revision (saved to drafts)