93 lines
2 KiB
C++
93 lines
2 KiB
C++
int sieve_size;
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bitset<10000001> bs;
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vector<int> pr;
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void sieve(int size) {
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sieve_size = size;
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bs.set(); bs[0] = bs[1] = 0;
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for (ll i = 2; i <= sieve_size; ++i) if (bs[i]) {
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for (ll j = i * i; j <= sieve_size; j += i) bs[j] = 0;
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pr.push_back(i);
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}
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}
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bool is_prime(ll N) {
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if (N <= sieve_size) return bs[N];
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for (int i = 0; i < pr.size() && pr[i] * pr[i] <= N; ++i) if (N % pr[i] == 0) return false;
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return true;
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}
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vector<ii> factorize(ll N) {
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vector<ii> factors;
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ll idx = 0, pf = pr[idx];
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while (N != 1 && pf * pf <= N) {
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if (N % pf == 0) {
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factors.emplace_back(pf, 0);
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while (N % pf == 0) { N /= pf; ++factors.back().s; }
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}
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pf = pr[++idx];
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}
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if (N != 1) factors.emplace_back(N, 1);
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return factors;
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}
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ll num_pf(ll N) {
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ll idx = 0, pf = pr[idx], ans = 0;
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while (N != 1 && pf * pf <= N)) {
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while (N % pf == 0) { N /= pf; ans++; }
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pf = pr[++idx];
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}
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return ans + (N != 1);
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}
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ll num_diff_pf(ll N) {
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ll idx = 0, pf = pr[idx], ans = 0;
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while (N != 1 && pf * pf <= N) {
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if (N % pf == 0) ans++;
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while (N % pf == 0) N /= pf;
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pf = pr[++idx];
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}
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return ans + (N != 1);
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}
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ll sum_pf(ll N) {
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ll idx = 0, pf = pr[idx], ans = 0;
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while (N != 1 && pf * pf <= N)) {
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while (N % pf == 0) { N /= pf; ans += pf; }
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pf = pr[++idx];
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}
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return ans + (N != 1) * N;
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}
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ll num_div(ll N) {
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ll idx = 0, pf = pr[idx], ans = 1;
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while (N != 1 && pf * pf <= N)) {
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ll power = 0;
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while (N % pf == 0) { N /= pf; ++power; }
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ans *= (power + 1);
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pf = pr[++idx];
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}
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return (N != 1) ? 2 * ans : ans;
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}
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ll sum_div(ll N) {
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ll idx = 0, pf = pr[idx], ans = 1;
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while (N != 1 && pf * pf <= N) {
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ll power = 0;
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while (N % pf == 0) { N /= pf; ++power; }
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ans *= ((ll)pow((double)pf, power + 1.0) - 1) / (pf - 1);
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pf = pr[++idx];
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}
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if (N != 1) ans *= ((ll)pow((double)N, 2.0) - 1) / (N - 1);
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return ans;
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}
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ll phi(ll N) {
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ll idx = 0, pf = pr[idx], ans = N;
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while (N != 1 && pf * pf <= N) {
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if (N % pf == 0) ans -= ans / pf;
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while (N % pf == 0) N /= pf;
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pf = pr[++idx];
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}
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return N != 1 ? ans - ans / N : ans;
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} |