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.
InputInput 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).
OutputFor each case, print the case number and the result.
Sample Input4
3
10
100
1000
Sample OutputCase 1: 1
Case 2: 5
Case 3: 83
Case 4: 947
#include<cstdio> #include<cmath> using namespace std; int main() { long long n; int t; scanf("%d",&t); for(int i=1;i<=t;i++) { scanf("%lld",&n); long long a1=sqrt(n); long long a2=sqrt(double(n/2)); printf("Case %d: %lld\n",i,n-a1-a2); } return 0; }