【规律】Farey Sums

 1 #pragma GCC optimize("Ofast,no-stack-protector")
 2 #pragma GCC optimize("O3")
 3 #pragma GCC optimize(2)
 4 #include <bits/stdc++.h>
 5 #define inf 0x3f3f3f3f
 6 #define linf 0x3f3f3f3f3f3f3f3fll
 7 #define pi acos(-1.0)
 8 #define nl "\n"
 9 #define pii pair<ll,ll>
10 #define ms(a,b) memset(a,b,sizeof(a))
11 #define FAST_IO ios::sync_with_stdio(NULL);cin.tie(NULL);cout.tie(NULL)
12 using namespace std;
13 typedef long long ll;
14 const int mod = 998244353;
15 ll qpow(ll x, ll y){ll s=1;while(y){if(y&1)s=s*x%mod;x=x*x%mod;y>>=1;}return s;}
16 //ll qpow(ll a, ll b){ll s=1;while(b>0){if(b%2==1)s=s*a;a=a*a;b=b>>1;}return s;}
17 inline int read(){int x=0,f=1;char ch=getchar();while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘)f=-1;ch=getchar();}while(ch>=‘0‘&&ch<=‘9‘) x=x*10+ch-‘0‘,ch=getchar();return x*f;}
18  
19 const int N = 1e4+5;
20  
21 ll pki[N];
22  
23 void get_pki()
24 {
25     for(int i=1;i<N;i++) pki[i] = i;
26     for(int i=2;i<N;i++){
27         if(pki[i]==i)for(int j=i;j<N;j+=i)
28             pki[j]=pki[j]/i*(i-1);
29         pki[i] += pki[i-1];
30     }
31 }
32  
33 int main()
34 {
35     get_pki();
36     int _, cas, n;
37     for(scanf("%d",&_);_--;)
38     {
39         scanf("%d",&cas);
40         scanf("%d",&n);
41         printf("%d %lld/2\n",cas,3*pki[n]-1);
42  
43     }
44  
45 }