CF236 B. Easy Number Challenge【求约数个数】_cf236b easy number challenge-优快云博客

本文链接：https://blog.youkuaiyun.com/nuanxin_520/article/details/51071847

本文介绍了一个名为 Easy Number Challenge 的问题，要求计算三个给定整数乘积的因子数量之和，并对结果求模。示例输入包括整数 a, b 和 c，输出为这些整数乘积的因子数量之和，模运算后的结果。通过预处理计算因子数量，实现高效求解。

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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:

$\text{[math]}$

Find the sum modulo 1073741824 (230).

Input

The first line contains three space-separated integers a, b and c (1 ≤ a, b, c ≤ 100).

Output

Print a single integer — the required sum modulo 1073741824 (230).

Note

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.

代码如下

#include<stdio.h>
const int MOD=1073741824;
const int MAX=1e6;
int a[MAX+10];
int pp()//判断一个数约数的个数
{   a[1]=1;
    for(int i=2; i<=MAX; i++)
    {   int q=i;
        a[i]=1;
        for(int j=2; j*j<=q; j++)//提高效率
          if(q%j==0)
            {  int s=1;
                while(q%j==0) s++,q/=j;
                a[i]*=s;
            }
           if(q>1)//当它的约数中有素数时
            a[i]*=2;
    }
}
int main()
{
    pp();
    int x,b,c,i,j,k;
    long long sum;
    while(~scanf("%d%d%d",&x,&b,&c))
    {
        sum=0;
        for(i=1; i<=x; i++)
            for(j=1; j<=b; j++)
                for(k=1; k<=c; k++)
                    sum=(sum+a[i*j*k]%MOD)%MOD;
        printf("%I64d\n",sum);

    }
}