#ifdef NACHIA #define _GLIBCXX_DEBUG #else #define NDEBUG #endif #include #include #include #include using i64 = long long; using u64 = unsigned long long; #define rep(i,n) for(int i=0; i void chmin(A& l, const A& r){ if(r < l) l = r; } template void chmax(A& l, const A& r){ if(l < r) l = r; } using namespace std; #include using Modint = atcoder::static_modint<998244353>; #include #include namespace nachia{ namespace internal{ // mod 2^64 constexpr unsigned long long PowerOfULongLong(unsigned long long a, unsigned long long i){ unsigned long long res = 1; while(i){ if(i&1){ res *= a; } i /= 2; a *= a; } return res; } } unsigned long long FloorOfKthRoot(unsigned long long real, unsigned long long k){ using u64 = unsigned long long; assert(k != 0); if(real <= 1) return real; if(k >= 64) return 1; if(k == 1) return real; struct Precalc{ // a^i <= x static constexpr bool lesseq(u64 a, int i, u64 x) { if (a == 0) return true; for(int j=0; j= 1; } unsigned long long BORDER[64]; constexpr Precalc() : BORDER() { for (int idx = 2; idx <= 63; idx++) { u64 l = 0, r = 1ull << 33; while (l + 1 < r) { u64 m = (l + r) / 2; if (lesseq(m, idx, ~0ull)) l = m; else r = m; } BORDER[idx] = r; } }; }; constexpr Precalc precalc; u64 l = 0, r = precalc.BORDER[k]; if(real < r) r = real; while (l + 1 < r) { u64 m = (l + r) / 2; if(internal::PowerOfULongLong(m, k) <= real) l = m; else r = m; } return l; } unsigned long long CeilOfKthRoot(unsigned long long real, unsigned long long k){ if(real <= 1) return real; if(k >= 64) return 2; if(k == 1) return real; unsigned long long x = FloorOfKthRoot(real, k); if(internal::PowerOfULongLong(x, k) != real) x++; return x; } } // namespace nachia namespace nachia{ long long CountSquarefree(long long n){ using i64 = long long; i64 s = 0; auto getMobius = [&](i64 n){ std::vector sieve(n+1, true); std::vector mu(n+1, 1); for(i64 i=2; i<=n; i++) if(sieve[i]){ mu[i] = -1; for(i64 j=i*i; j<=n; j+=i) sieve[j] = false; for(i64 j=i*2; j<=n; j+=i) mu[j] = -mu[j]; for(i64 j=i*i; j<=n; j+=i*i) mu[j] = 0; } return mu; }; if(n <= 4000){ auto mu = getMobius(n+1); for(i64 i=1; i*i<=n; i++) s += n/(i*i) * mu[i]; return s; } i64 I = nachia::FloorOfKthRoot(n, 5); i64 D = nachia::FloorOfKthRoot(n/(I+1), 2); auto mu = getMobius(D+1); std::vector Mf(D+1); for(i64 i=1; i<=D; i++) Mf[i] = Mf[i-1] + mu[i]; std::vector Md(I+1); for(i64 i=I; i>=1; i--){ i64 m = 1; i64 x = nachia::FloorOfKthRoot(n/i, 2); i64 Dx = nachia::FloorOfKthRoot(x, 2); i64 Rx = x / (Dx+1); i64 r = 2; for( ; i*r*r<=I; r++) m -= Md[i*r*r]; for( ; r<=Rx; r++) m -= Mf[x/r]; for(i64 d=1; d<=Dx; d++) m -= mu[d] * (x/d - Rx); Md[i] = m; s += m; } for(i64 i=1; i<=D; i++) s += mu[i] * (n/(i*i) - I); return s; } } // namespace nachia void testcase(){ i64 N; cin >> N; N /= 2; if(N < 6){ cout << "0\n"; return; } i64 R = 0; for(i64 d=1ll<<20; d>=1; d>>=1) if((R+d)*(R+d) <= N) R += d; i64 L = R; i64 sqfree_border = min(R, 30000); vector Sqfree(sqfree_border + 1); for(i64 i=1; i<=sqfree_border; i++) Sqfree[i] = nachia::CountSquarefree(N/i); vector sqfree(N / sqfree_border + 1, 0); for(i64 i=1; i*sqfree_border<=N; i+=2) sqfree[i] += 1; for(i64 p=2; p*p<=N/sqfree_border; p++) if(sqfree[p*p]){ for(i64 q=1; p*p*q<=N/sqfree_border; q++) sqfree[p*p*q] = 0; } for(i64 i=1; i=1; i--) Sqfree[i] -= sqfree_access(i*2); if(N <= 5000000){ vector A(N+1); for(i64 n=1; n*n<=N; n++){ for(i64 m=1; m(R, 10000); i64 P = N / Q; i64 ans = 0; for(i64 n=1; n*n<=P; n++){ for(i64 m=1; m Q2(Q+1); for(i64 q=1; q<=Q; q++){ i64 p = N / q; while(R*R > p) R--; while(L*L*2 > p) L--; i64 f = L * (L - 1) / 2; for(i64 i=L+1; i<=R; i++) f += p / i - i; Q2[q] = f; } for(i64 q=1; q