# [SDOi2012]Longge的问题 BZOJ2705 数学

SDOi2012

## 题目描述

Longge的数学成绩非常好，并且他非常乐于挑战高难度的数学问题。现在问题来了：给定一个整数N，你需要求出∑gcd(i, N)(1<=i <=N)。

## 输入输出样例

6

15

## 说明

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cstdlib>
#include<cstring>
#include<string>
#include<cmath>
#include<map>
#include<set>
#include<vector>
#include<queue>
#include<bitset>
#include<ctime>
#include<time.h>
#include<deque>
#include<stack>
#include<functional>
#include<sstream>
//#include<cctype>
//#pragma GCC optimize(2)
using namespace std;
#define maxn 2000005
#define inf 0x7fffffff
//#define INF 1e18
#define rdint(x) scanf("%d",&x)
#define rdllt(x) scanf("%lld",&x)
#define rdult(x) scanf("%lu",&x)
#define rdlf(x) scanf("%lf",&x)
#define rdstr(x) scanf("%s",x)
#define mclr(x,a) memset((x),a,sizeof(x))
typedef long long  ll;
typedef unsigned long long ull;
typedef unsigned int U;
#define ms(x) memset((x),0,sizeof(x))
const long long int mod = 1e9 + 7;
#define Mod 1000000000
#define sq(x) (x)*(x)
#define eps 1e-5
typedef pair<int, int> pii;
#define pi acos(-1.0)
//const int N = 1005;
#define REP(i,n) for(int i=0;i<(n);i++)
typedef pair<int, int> pii;

inline int rd() {
int x = 0;
char c = getchar();
bool f = false;
while (!isdigit(c)) {
if (c == '-') f = true;
c = getchar();
}
while (isdigit(c)) {
x = (x << 1) + (x << 3) + (c ^ 48);
c = getchar();
}
return f ? -x : x;
}

ll gcd(ll a, ll b) {
return b == 0 ? a : gcd(b, a%b);
}
int sqr(int x) { return x * x; }

/*ll ans;
ll exgcd(ll a, ll b, ll &x, ll &y) {
if (!b) {
x = 1; y = 0; return a;
}
ans = exgcd(b, a%b, x, y);
ll t = x; x = y; y = t - a / b * y;
return ans;
}
*/
ll N;
ll Phi(ll x) {
ll ans = x;
for (ll i = 2; i <= (ll)sqrt(x); i++) {
if (x%i == 0) {
ans = ans / i * (i - 1);
while (x%i == 0)x /= i;
}

}
if (x > 1)ans = ans / x * (x - 1);
return ans;
}

int main()
{
//	ios::sync_with_stdio(0);
rdllt(N);
ll ans = 0;
for (ll i = 1; i <= sqrt(N); i++) {
if (N%i == 0) {
if (i*i == N) {
ans += Phi(i)*i; continue;
}
else {
ans += Phi(i)*(N / i) + Phi(N / i)*i;
}
}
}
cout << ans << endl;
return 0;
}


EPFL - Fighting
posted @ 2019-02-11 20:15  NKDEWSM  阅读(167)  评论(0编辑  收藏  举报