【数学】Mobius函数

质因数分解法求Mobius函数

const int MAXN = 1e6 + 10;
int p[MAXN], ptop;
int pm[MAXN], pk[MAXN], mu[MAXN];

void sieve(int n) {
    memset(pm, 0, sizeof(pm[0]) * (n + 1));
    ptop = 0, pm[1] = 1, pk[1] = 1, mu[1] = 1;
    for(int i = 2; i <= n; ++i) {
        if(!pm[i]) {
            p[++ptop] = i, pm[i] = i;
            pk[i] = i, mu[i] = -1;
        }
        for(int j = 1, t; j <= ptop && (t = i * p[j]) <= n; ++j) {
            pm[t] = p[j];
            if(i % p[j]) {
                pk[t] = pk[p[j]];
                mu[t] = mu[i] * mu[p[j]];
            } else {
                pk[t] = pk[i] * p[j];
                mu[t] = (pk[t] == t) ? 0 : mu[t / pk[t]] * mu[pk[t]];
                break;
            }
        }
    }
}