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    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

    https://blog.csdn.net/strangedbly/article/details/50908522

    #include<map>
    #include<stack>
    #include<queue>
    #include<math.h>
    #include<vector>
    #include<string>
    #include<stdio.h>
    #include<iostream>
    #include<string.h>
    #include<algorithm>
    #define mem(a,b) memset(a,b,sizeof(a))
    #define maxn 1100000
    #define maxm 1000000000005
    #define mod 1000000007
    #define ll long long
    #define inf 0x3f3f3f3f
    using namespace std;
    int main(){
        int t,test=0;scanf("%d",&t);
        while(t--){
            ll n;scanf("%lld",&n);
            ll ans=0;
            ans=(ll)sqrt(n*1.0);
            ans+=(ll)sqrt(n/2.0);
            printf("Case %d: %lld
    ",++test,n-ans);
        }
    }

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  • 原文地址:https://www.cnblogs.com/da-mei/p/9053230.html
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