Number Challenge
题意翻译
题意:记d(i)表示i的约数个数,输入a,b,c;
求
![](https://cdn.luogu.org/upload/vjudge_pic/CF235E/6b4d9893ce96bd0459ff1289a8bf3491052ac12a.png)%mod(1073741824($2^{30}$))的值。
Translated by @Roots
题目描述
Let's denote $ d(n) $ as the number of divisors of a positive integer $ n $ . You are given three integers $ a $ , $ b $ and $ c $ . Your task is to calculate the following sum:
![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF235E/6b4d9893ce96bd0459ff1289a8bf3491052ac12a.png)Find the sum modulo $ 1073741824 $ $ (2^{30}) $ .
输入输出格式
输入格式
The first line contains three space-separated integers $ a $ , $ b $ and $ c $ ( $ 1<=a,b,c<=2000 $ ).
输出格式
Print a single integer — the required sum modulo $ 1073741824 $ $ (2^{30}) $ .
输入输出样例
输入样例 #1
2 2 2
输出样例 #1
20
输入样例 #2
4 4 4
输出样例 #2
328
输入样例 #3
10 10 10
输出样例 #3
11536
说明
For the first example.
- $ d(1·1·1)=d(1)=1 $ ;
- $ d(1·1·2)=d(2)=2 $ ;
- $ d(1·2·1)=d(2)=2 $ ;
- $ d(1·2·2)=d(4)=3 $ ;
- $ d(2·1·1)=d(2)=2 $ ;
- $ d(2·1·2)=d(4)=3 $ ;
- $ d(2·2·1)=d(4)=3 $ ;
- $ d(2·2·2)=d(8)=4 $ .
So the result is $ 1+2+2+3+2+3+3+4=20 $ .