LightOJ - 1336 Sigma Function

Sigma function is an interesting function in Number Theory. It is denoted by the Greek letter Sigma (σ). This function actually denotes the sum of all divisors of a number. For example σ(24) = 1+2+3+4+6+8+12+24=60. Sigma of small numbers is easy to find but for large numbers it is very difficult to find in a straight forward way. But mathematicians have discovered a formula to find sigma. If the prime power decomposition of an integer is

Then we can write,

For some n the value of σ(n) is odd and for others it is even. Given a value n, you will have to find how many integers from 1 to n have even value of σ.

Input

Input starts with an integer T (≤ 100), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n ≤ 1012).

Output

For each case, print the case number and the result.

Sample Input

4

3

10

100

1000

Sample Output

Case 1: 1

Case 2: 5

Case 3: 83

Case 4: 947

题意 。求1-n 中σ(n) 的偶数和有几个。

只要存在一个pi,ei都为奇数的pi^ei,就能使sum为偶数

2是唯一一个偶素数

推荐博客https://www.cnblogs.com/Ritchie/p/5299970.html

#include <iostream>
#include <string>
#include <cstring>
#include <algorithm>
#include <cstdio>
#include <cmath>
using namespace std;
#define ll long long
int main()
{
    ll t,cnt=0;
    cin>>t;
    while(t--)
    {
        ll n,a,b;
        cnt++;
        cin>>n;
        a=sqrt(n);
        b=sqrt(n/2);
        cout<<"Case "<<cnt<<": "<<n-a-b<<endl;
    }return 0;
}