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constexpr ll N = 10'000'000;
ll smallest[N], power[N], sieved[N];
vector<ll> primes;
//wird aufgerufen mit (p^k, p, k) für prime p
ll mu(ll pk, ll p, ll k) {return -(k == 1);}
ll phi(ll pk, ll p, ll k) {return pk - pk / p;}
ll div(ll pk, ll p, ll k) {return k+1;}
ll divSum(ll pk, ll p, ll k) {return (pk*p+1) / (p - 1);}
ll square(ll pk, ll p, ll k) {return k % 2 ? pk / p : pk;}
ll squareFree(ll pk, ll p, ll k) {return k % 2 ? pk : 1;}
void sieve() { // O(N)
smallest[1] = power[1] = sieved[1] = 1;
for (ll i = 2; i < N; i++) {
if (smallest[i] == 0) {
primes.push_back(i);
for (ll pk = i, k = 1; pk < N; pk *= i, k++) {
smallest[pk] = i;
power[pk] = pk;
sieved[pk] = mu(pk, i, k); // Aufruf ändern!
}}
for (ll j = 0; i * primes[j] < N && primes[j] < smallest[i]; j++) {
ll k = i * primes[j];
smallest[k] = power[k] = primes[j];
sieved[k] = sieved[i] * sieved[primes[j]];
}
if (i * smallest[i] < N && power[i] != i) {
ll k = i * smallest[i];
smallest[k] = smallest[i];
power[k] = power[i] * smallest[i];
sieved[k] = sieved[power[k]] * sieved[k / power[k]];
}}}
ll naive(ll n) { // O(sqrt(n))
ll res = 1;
for (ll p = 2; p * p <= n; p++) {
if (n % p == 0) {
ll pk = 1;
ll k = 0;
do {
n /= p;
pk *= p;
k++;
} while (n % p == 0);
res *= mu(pk, p, k); // Aufruf ändern!
}}
return res;
}
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