#include #include #include #include #include #include #include #include #include #include #include using namespace std; using u8 = unsigned char; using i64 = long long; using u64 = long long unsigned; int isqrt(i64 n) { return sqrtl(n); } i64 divide(i64 n, i64 d) { return double(n) / d; } __attribute__((target("avx"), optimize("O3", "unroll-loops"))) pair< vector, vector > prime_counts(const i64 N) { const int v = isqrt(N); vector smalls(v + 1); vector larges(v + 1); for (int i = 1; i <= v; ++i) smalls[i] = i - 1; for (int i = 1; i <= v; ++i) larges[i] = N / i - 1; for (int p = 2, pcnt = 0; p <= v; ++p) if (smalls[p] > smalls[p - 1]) { const i64 M = N / p, q = i64(p) * p; const int w = v / p, l = min(v, N / q); for (int i = 1; i <= w; ++i) larges[i] -= larges[i * p] - pcnt; const int t = min(isqrt(M), l); for (int i = w + 1; i <= t; ++i) larges[i] -= smalls[divide(M, i)] - pcnt; for (int i = l, j = M / l; i > t; ++j) { int c = smalls[j]; while (j + 1 <= v && smalls[j + 1] == c) ++j; c -= pcnt; for (int e = max(t, divide(M, j + 1)); i > e; --i) larges[i] -= c; } for (int i = v, j = v / p; j >= p; --j) { const int c = smalls[j] - pcnt; for (int e = j * p; i >= e; --i) smalls[i] -= c; } ++pcnt; } return make_pair(smalls, larges); } using u8 = unsigned char; vector prime_sieve(int N) { if (N <= 1) return vector(); const int sieve_size = 32 << 10; static u8 block[sieve_size]; const int v = sqrt(N), vv = sqrt(v); vector is_prime(v + 1, 1); vector> sprimes; for (int i = 2; i <= vv; ++i) if (is_prime[i]) { for (int j = i * i; j <= v; j += i) is_prime[j] = 0; } for (int i = 3; i <= v; i += 2) if (is_prime[i]) sprimes.emplace_back(i, i * i / 2); const int rsize = N > 60184 ? N / (log(N) - 1.1) : max(1., N / (log(N) - 1.11)) + 1; vector primes(1, 2); primes.resize(rsize); int psize = 1; auto* pblock = block - 1; for (int beg = 1; beg < (N + 1) / 2; beg += sieve_size, pblock -= sieve_size) { int end = min(beg + sieve_size, (N + 1) / 2); fill(block, block + sieve_size, 1); for (int i = 0; i < int(sprimes.size()); ++i) { int p, next; tie(p, next) = sprimes[i]; if (p * p > N) break; for (; next < end; next += p) pblock[next] = 0; sprimes[i].second = next; }; for (int i = beg; i < end; ++i) if (pblock[i]) primes[psize++] = 2 * i + 1; } assert(psize <= int(primes.size())); primes.resize(psize); return primes; } __attribute__((target("avx"), optimize("O3", "unroll-loops"))) i64 prime_pi(const i64 N) { if (N <= 1) return 0; if (N == 2) return 1; const int v = isqrt(N); int s = (v + 1) / 2; vector smalls(s); for (int i = 1; i < s; ++i) smalls[i] = i; vector roughs(s); for (int i = 0; i < s; ++i) roughs[i] = 2 * i + 1; vector larges(s); for (int i = 0; i < s; ++i) larges[i] = (N / (2 * i + 1) - 1) / 2; vector skip(v + 1); const auto divide = [] (i64 n, i64 d) -> int { return double(n) / d; }; const auto half = [] (int n) -> int { return (n - 1) >> 1; }; int pc = 0; for (int p = 3; p <= v; p += 2) if (!skip[p]) { int q = p * p; if (i64(q) * q > N) break; skip[p] = true; for (int i = q; i <= v; i += 2 * p) skip[i] = true; int ns = 0; for (int k = 0; k < s; ++k) { int i = roughs[k]; if (skip[i]) continue; i64 d = i64(i) * p; larges[ns] = larges[k] - (d <= v ? larges[smalls[d >> 1] - pc] : smalls[half(divide(N, d))]) + pc; roughs[ns++] = i; } s = ns; for (int i = half(v), j = ((v / p) - 1) | 1; j >= p; j -= 2) { int c = smalls[j >> 1] - pc; for (int e = (j * p) >> 1; i >= e; --i) smalls[i] -= c; } ++pc; } larges[0] += i64(s + 2 * (pc - 1)) * (s - 1) / 2; for (int k = 1; k < s; ++k) larges[0] -= larges[k]; for (int l = 1; l < s; ++l) { int q = roughs[l]; i64 M = N / q; int e = smalls[half(M / q)] - pc; if (e < l + 1) break; i64 t = 0; for (int k = l + 1; k <= e; ++k) t += smalls[half(divide(M, roughs[k]))]; larges[0] += t - i64(e - l) * (pc + l - 1); } return larges[0] + 1; } int main() { u64 N; while (~scanf("%llu", &N)) { const auto pc = prime_counts(N + 1); u64 v = isqrt(N + 1); auto primes = prime_sieve(v + 10); std::vector isp(v + 1, -1); auto count = [&] (u64 n) -> u64 { if (n <= v) return pc.first[n]; else { size_t i = N / (n - 1); u64 q = (N + 1) / i; assert(q <= n && n <= q + 1); if (q == n || (n >= 4 && n % 2 == 0)) { return (i > v) ? pc.first[q] : pc.second[i]; } if (isp[i] < 0) { isp[i] = 1; for (size_t j = 1; j < primes.size(); ++j) { u64 p = primes[j]; if (p * p > n) break; if (n % p != 0) continue; isp[i] = 0; break; } } return pc.second[i] + isp[i]; } }; function rec = [&] (u64 phi, size_t beg) -> u64 { u64 ret = count(phi + 1) - beg; for (size_t i = beg; i < primes.size(); ++i) { u64 p = primes[i]; if ((p - 1) * p > phi) break; u64 nphi = phi / (p - 1); while (nphi + 1 > u64(primes[i])) { ret += rec(nphi, i + 1) + 1; nphi /= p; } } return ret; }; u64 ans = rec(N, 0) + 1; printf("%llu\n", ans); } return 0; }