BZOJ2721 [Violet 5]樱花

先令n! = a：

1 / x + 1 / y = 1 / a  =>  x = y * a / (y - a)

再令 k = y - a：

于是x = a + a ^ 2 / k  =>  k | a ^ 2

故等价于求a ^２的约数个数

素数筛一下什么的就好了嘛

 /**************************************************************
     Problem: 2721
     User: rausen
     Language: C++
     Result: Accepted
     Time:588 ms
     Memory:2408 kb
 ****************************************************************/

 #include <cstdio>

 using namespace std;
 typedef long long ll;
 const int N = ;
 const int Cnt = ;
 const int mod = ;

 int n;
 bool F[N];
 int cnt, p[Cnt], c[Cnt];
 ll ans = ;

 int main() {
     int i, j, t;
     scanf("%d\n", &n);
     for (i = ; i < N; ++i) {
         if (!F[i]) p[++cnt] = i;
         for (j = ; j <= cnt && p[j] * i < N; ++j) {
             F[p[j] * i] = ;
             if (p[j] % i == ) break;
         }
     }
     for (i = ; i <= cnt; ++i)
         for (j = p[i]; j <= n; j += p[i])
             for (t = j; t % p[i] == ; t /= p[i]) ++c[i];
     for (i = ; i <= cnt; ++i)
         (ans *= (c[i] <<  | )) %= mod;
     printf("%lld\n", ans);
     return ;
 }