Number Challenge

题面翻译

题意:记d(i)表示i的约数个数，输入a,b,c; 求 %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:

Find the sum modulo $1073741824$ $(2^{30})$ .

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 $1073741824$ $(2^{30})$ .

样例 #1

样例输入 #1

2 2 2

样例输出 #1

20

样例 #2

样例输入 #2

4 4 4

样例输出 #2

328

样例 #3

样例输入 #3

10 10 10

样例输出 #3

11536

提示

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 $1+2+2+3+2+3+3+4=20$ .