POJ - 2154 Color——Polya+欧拉函数优化

ans = 1/n*∑(0<=i && i < n)(n^gcd(i, n))

       = 1/n*∑(0<=i && i < n && n%i == 0)(euler(i) * n^i)

       = ∑(0<=i && i < n && n%i == 0)(euler(i) * n^(i-1))

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;
int euler(int x) {
    int ans = x;
    for (int i = 2; i * i <= 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;
}
ll ipow(ll a, int n, int mod) {
    ll ans = 1;
    while (n) {
        if (n & 1) ans = (ans * a) % mod;
        a = (a * a) % mod;
        n >>= 1;
    }
    return ans;
}
int main() {
    int x, n, p;
    scanf("%d", &x);
    while (x--) {
        scanf("%d%d", &n, &p);
        ll ans = 0;
        for (int i = 1; i * i <= n; i++) {
            if (i * i == n) ans = (ans + ipow(n, i-1, p)*euler(i)) % p;
            else if (n % i == 0) {
                ans = (ans + ipow(n, i-1, p)*euler(n/i) + ipow(n, n/i-1, p) * euler(i)) % p;
            }
        }
        printf("%lld\n", ans);
    }
    return 0;
}