pre ios ont c代碼 euler iostream spa seve size

Description

Longge is good at mathematics and he likes to think about hard mathematical problems which will be solved by some graceful algorithms. Now a problem comes: Given an integer N(1 < N < 2^31),you are to calculate ∑gcd(i, N) 1<=i <=N.
"Oh, I know, I know!" Longge shouts! But do you know? Please solve it.

Input

Input contain several test case.
A number N per line.

Output

For each N, output ,∑gcd(i, N) 1<=i <=N, a line

Sample Input

2
6

Sample Output

3
15
解題思路：
AC代碼：

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <map>
 5 #include <vector>
 6
 
 #include <set>
 7 using namespace std;
 8 typedef long long LL;
 9 const int maxn = 1e6+5;
10 LL n, ans;
11 LL get_Euler(LL x){
12     LL res = x;
13     for(LL i = 2LL; i * i <= x; ++i) {
14         if(x % i == 0) {
15             res = res / i * (i - 1);
16             while(x % i == 0
 
) x /= i;
17         }
18     }
19     if(x > 1LL) res = res / x * (x - 1);
20     return res;
21 }
22 
23 int main(){
24     while(cin >> n) {
25         ans = 0LL;
26         for (LL i = 1LL; i * i <= n; ++i) {
27             if(n % i == 0) {
28                 ans += i * get_Euler(n / i);
29                 if(i * i != n) ans += n / i * get_Euler(i); ///避免重復計數
30             }
31          }
32          cout << ans << endl;
33     }
34     return 0;
35 }

題解報告：poj 2480 Longge's problem（歐拉函數）