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Harmonic Number

In mathematics, the n^th harmonic number is the sum of the reciprocals of the first n natural numbers:

In this problem, you are given n, you have to find H_n.

Input

Input starts with an integer T (≤ 10000), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n ≤ 10⁸).

Output

For each case, print the case number and the n^th harmonic number. Errors less than 10^-8 will be ignored.

Sample Input

12

1

2

3

4

5

6

7

8

9

90000000

99999999

100000000

Sample Output

Case 1: 1

Case 2: 1.5

Case 3: 1.8333333333

Case 4: 2.0833333333

Case 5: 2.2833333333

Case 6: 2.450

Case 7: 2.5928571429

Case 8: 2.7178571429

Case 9: 2.8289682540

Case 10: 18.8925358988

Case 11: 18.9978964039

Case 12: 18.9978964139

求1+1/2+1/3+...+1/n

#include<bits/stdc++.h>
#define e 0.57721566490153286060651209
using namespace std;
typedef long long ll;

double a[10005];
int main()
{
    int tt=0,t,n,i;
    a[1]=1;
    for(i=2;i<=10000;i++){
        a[i]=a[i-1]+1.0/i;
    }
    scanf("%d",&t);
    while(t--){
        scanf("%d",&n);
        if(n<=10000){
            printf("Case %d: %.10lf
",++tt,a[n]);
        }
        else{
            double ans=log(n)+e+1.0/(2*n);
            printf("Case %d: %.10lf
",++tt,ans);
        }
    }
    return 0;
}

Harmonic Number (II)

I was trying to solve problem '1234 - Harmonic Number', I wrote the following code

long long H( int n ) {
    long long res = 0;
    for( int i = 1; i <= n; i++ )
        res = res + n / i;
    return res;
}

Yes, my error was that I was using the integer divisions only. However, you are given n, you have to find H(n) as in my code.

Input

Input starts with an integer T (≤ 1000), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n < 2³¹).

Output

For each case, print the case number and H(n) calculated by the code.

Sample Input

11

1

2

3

4

5

6

7

8

9

10

2147483647

Sample Output

Case 1: 1

Case 2: 3

Case 3: 5

Case 4: 8

Case 5: 10

Case 6: 14

Case 7: 16

Case 8: 20

Case 9: 23

Case 10: 27

Case 11: 46475828386

 

求n+n/2+n/3+...+n/n

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

int main()
{
    int tt=0,T,i;
    ll n;
    cin>>T;
    while(T--)
    {
        cin>>n;
        int m=sqrt(n);
        ll sum=0;
        for(i=1;i<=m;i++){
            sum+=n/i;
        }
        for(i=1;i<=m;i++){
            sum+=(n/i-n/(i+1))*i;
        }
        if(m==n/m) sum-=m;
        cout<<"Case "<<++tt<<": "<<sum<<endl;
    }
    return 0;
}