#include #include template struct Mobius { std::array mobius; Mobius() : mobius{} { mobius[1] = 1; std::array not_prime{}; for (int p = 2; p <= M; ++p) { if (not_prime[p]) continue; for (int v = M / p, vp = v * p; v; --v, vp -= p) { mobius[vp] = -mobius[v]; not_prime[vp] = true; } } } int operator[](int i) const { return mobius[i]; } }; constexpr int M = 1000000; Mobius mobius; long long count_square_2_3_free(long long n) { const int q = std::sqrt(n); long long res = 0; for (int i = 1; i <= q; ++i) if (mobius[i] and i % 2 and i % 3) { long long v1 = double(n + 1LL * i * i) / (6LL * i * i); long long v5 = double(n + 5LL * i * i) / (6LL * i * i); res += mobius[i] * (v1 + v5); } return res; } #include #include int main() { long long l; int n; std::cin >> l >> n; std::array, 40> cnt{}; for (int i = 0; i < n; ++i) { long long e; std::cin >> e; int p2 = 0, p3 = 0; while (e % 2 == 0) e /= 2, ++p2; while (e % 3 == 0) e /= 3, ++p3; cnt[p2][p3] = true; } long long ans = 0; for (int p2 = 0; p2 < 40; ++p2) for (int p3 = 0; p3 < 30; ++p3) { int x00 = cnt[p2][p3]; int x10 = p2 and cnt[p2 - 1][p3]; int x01 = p3 and cnt[p2][p3 - 1]; int x11 = p2 and p3 and cnt[p2 - 1][p3 - 1]; if (x00 xor x01 xor x10 xor x11) { long long v = 1; for (int e = p2; e--;) v *= 2; for (int e = p3; e--;) v *= 3; long long lim = l / v; ans += count_square_2_3_free(lim); } } std::cout << ans << '\n'; }