1.题目
In number theory, Euler’s totient function φ(n) counts the positive integers up to a given integer n that are relatively prime to n. It can be defined more formally as the number of integers k in the range 1≤k≤n for which the greatest common divisor gcd is equal to 1.
For example, \varphi(9) = 6 because 1, 2, 4, 5, 7 and 8 are coprime with 9. As another example, \varphi(1) = 1 since for n = 1 the only integer in the range from 1 to n is 1 itself, and \gcd(1, 1) = 1.
A composite number is a positive integer that can be formed by multiplying together two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. So obviously 1 and all prime numbers are not composite number.
In this problem, given integer k, your task is to find the k-th smallest positive integer n, that \varphi(n) is a composite number.
Input
The first line of the input contains an integer T(1\leq T\leq100000), denoting the number of test cases.
In each test case, there is only one integer k(1\leq k\leq 10^9).
Output
For each test case, print a single line containing an integer, denoting the answer.
Sample Input
2
1
2
Sample Output
5
7
2.代码
#include<iostream>
#include<algorithm>
using namespace std;
int main()
{
int t;
cin>>t;
while(t--)
{
int k;
cin>>k;
if(k==1)
cout<<'5'<<endl;
else if(k==2)
cout<<'7'<<endl;
else
cout<<k+5<<endl;
}
return 0;
}