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
#include<iostream> #include<cstdio> #include<cstring> #include<sstream> #include<algorithm> #include<queue> #include<vector> #include<cmath> #include<map> #include<stack> #include<set> #include<fstream> #include<memory> #include<list> #include<string> using namespace std; typedef long long LL; typedef unsigned long long ULL; #define MAXN 1000010 #define LLL 1000000000 #define INF 1000000009 /* 给一个公式，将一个数表示为所有素因子等比数列 求前e个 的乘积 求小于n的数中为奇数的个数 数据很大不能打表。。 当p为偶数 ,p的次方为偶数，加上p的0次方 最后得出奇数不成立 当P为奇数，P的次方为奇数，要有偶数个奇数相加才能得出偶数，要求e为奇数 当所有的 p和e中总是存在任何一个不为奇数的时候，结果为奇数 e为偶数 平方数 后面乘某些数 后面的数字是2的几次方的时候仍然成立 （2是唯一的素偶数） 所有个数为 平方数||2*平方数 */ int main() { LL T,n; scanf("%lld", &T); for(LL cas=1;cas<=T;cas++) { scanf("%lld", &n); LL t1 = sqrt(n*1.0); LL t2 = sqrt(n*0.5); printf("Case %lld: %lld\n",cas, n - t1 - t2); } return 0; }