Sigma Function LightOJ

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

通过打表找出因子和是奇数的规律，当它是x^2 或者是 2*x^2 的形式时为奇数，排除这些其余即为偶数，题目所给的式子没有用上。。。。。。（网上有通过该表达式来推出结果的）

#include<cstdio>#include<cstring>#include<cmath>#include<cstdlib>#include<queue>#include<algorithm>#define ll long long#define inf 0x3f3f3f3f#define manx 1000007  // 1e6+7using namespace std;int main(){    int t;    scanf("%d",&t);    int k = 1;    while( t--)    {        ll a,b,n;        scanf("%lld",&n);        a = (ll)sqrt(n);        b = (ll)sqrt(n*1.0/2.0);        printf("Case %d: %lld\n",k++,n - ( a + b) );    }    return 0;}