HDU 2582 - f(n) (规律)
思路
打表。可得如果一个数是$x^n$,Gcd(k) = x$
如果是素数,本身。
其他的话是1.
思路
#include <stack>
#include <cstdio>
#include <list>
#include <cassert>
#include <set>
#include <iostream>
#include <string>
#include <vector>
#include <queue>
#include <functional>
#include <cstring>
#include <algorithm>
#include <cctype>
#include <string>
#include <map>
#include <cmath>
using namespace std;
#define LL long long
#define ULL unsigned long long
#define SZ(x) (int)x.size()
#define Lowbit(x) ((x) & (-x))
#define MP(a, b) make_pair(a, b)
#define MS(arr, num) memset(arr, num, sizeof(arr))
#define PB push_back
#define X first
#define Y second
#define ROP freopen("input.txt", "r", stdin);
#define MID(a, b) (a + ((b - a) >> 1))
#define LC rt << 1, l, mid
#define RC rt << 1|1, mid + 1, r
#define LRT rt << 1
#define RRT rt << 1|1
const double PI = acos(-1.0);
const int INF = 0x3f3f3f3f;
const double eps = 1e-8;
const int MAXN = 1e6 + 10;
const int MOD = 1e9 + 7;
const int dir[][2] = { {-1, 0}, {0, -1}, { 1, 0 }, { 0, 1 } };
const int hash_size = 4e5 + 10;
int cases = 0;
typedef pair<int, int> pii;
int vis[MAXN];
LL sum[MAXN];
void Prime()
{
int m = (int)sqrt(MAXN + 0.5);
for (int i = 2; i <= m; i++) if (!vis[i])
for (int j = i*i; j < MAXN; j += i) vis[j] = 1;
}
map<int, int> mp;
void Handle()
{
Prime();
int k = sqrt(MAXN + 0.5);
for (int i = 2; i <= k; i++)
{
LL tmp = 1;
if (mp.count(i) || vis[i]) continue;
while (tmp*i < MAXN) tmp *= i, mp[tmp] = i;
}
for (int i = 3; i < MAXN; i++)
{
if (mp.count(i)) sum[i] = sum[i-1] + mp[i];
else if (!vis[i]) sum[i] = sum[i-1] + i;
else sum[i] = sum[i-1] + 1;
}
}
int main()
{
Handle();
int n;
while (~scanf("%d", &n)) printf("%lld\n", sum[n]);
return 0;
}