27E - Number With The Given Amount Of Divisors

假设P(i)代表某个素数,a(i)代表这个素数的幂

那么任何一个数都可以分解成 ( P(1)^a(1) )*( P(2)^a(2) )*( P(3)^a(3) )*.............*( P(k)^a(k) )

而且这个数的约数的数量为 (a(1)+1)*(a(2)+1)*(a(3)+1)*.............*(a(k)+1) (包括该数本身

</pre><pre name="code" class="html">#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<map>
#include<set>
#include<vector>
#include<stack>
#include<queue>
#include<algorithm>
#include<cmath>

#define ll long long
#define ULL unsigned long long
using namespace std;
const int INF=0x3f3f3f3f;
const long long LINF=ceil(1e18);
int p[11]={1,2,3,5,7,11,13,17,19,23,29};
ll ans;

void dfs(int x,int n,long long M)
{
    if(n==1)
    {
        ans=min(ans,M);
        return;
    }
    long long k=p[x];
    for(int l=1;l<n&&k<LINF;l++,k=k*p[x])
        if(n%(l+1)==0)
        {
            if(M*k>LINF||M*k<=0)
            break;
            dfs(x+1,n/(l+1),M*k);
        }
}

int main()
{
    //freopen("data.in","r",stdin);
    int n;
    while(~scanf("%d",&n))
    {
        ans=LINF;
        dfs(1,n,1);
        printf("%lld\n",ans);
    }
    return 0;
}