#include #include using namespace std; namespace my{ #define eb emplace_back #define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__) #define FO(n) for(ll ij=n;ij-->0;) #define FOR(i,...) for(auto[i,i##stop,i##step]=range(0,__VA_ARGS__);isync_with_stdio(0);cout<r{0,0,1};ll I=0;((r[I++]=a),...);if(!s&&I==1)swap(r[0],r[1]);r[0]-=s;if(s)r[2]*=-1;return r;} constexpr char newline=10; constexpr char space=32; auto ceil(auto x,auto y){if(y<0)x=-x,y=-y;return x<=0?x/y:(x-1)/y+1;} auto max(auto...a){return max(initializer_list>{a...});} templatestruct pair{ A a;B b; pair()=default; pair(A a,B b):a(a),b(b){} pair(const std::pair&p):a(p.first),b(p.second){} auto operator<=>(const pair&)const=default; pair operator+(const pair&p)const{return{a+p.a,b+p.b};} friend istream&operator>>(istream&i,pair&p){return i>>p.a>>p.b;} friend ostream&operator<<(ostream&o,const pair&p){return o<ostream&operator<<(ostream&o,const std::pair&p){return o<auto pack_kth(const auto&...a){return get(make_tuple(a...));} templateauto pack_slice_impl(index_sequence, const auto&...a){return array{get(forward_as_tuple(a...))...};} templateauto pack_slice(const auto&...a){return pack_slice_impl(make_index_sequence{},a...);} templateconcept vectorial=is_base_of_v,V>; templatestruct vec_attr{using core_type=T;static constexpr int rank=0;}; templatestruct vec_attr{using core_type=typename vec_attr::core_type;static constexpr int rank=vec_attr::rank+1;}; templateusing core_t=vec_attr::core_type; templateistream&operator>>(istream&i,vector&v){fe(v,e)i>>e;return i;} templateostream&operator<<(ostream&o,const vector&v){fe(v,e)o<?newline:space);return o;} templatestruct vec:vector{ using vector::vector; vec(const vector&v){vector::operator=(v);} templaterequires(sizeof...(A)>=3)vec(A...a){const ll n=sizeof...(a)-1;auto t=pack_slice(a...);ll s[n];fo(i,n)s[i]=t[i];*this=make_vec(s,pack_kth(a...));} templatestatic auto make_vec(const ll(&s)[n],T x){if constexpr(i==n-1)return vec(s[i],x);else{auto X=make_vec(s,x);return vec(s[i],X);}} vec&operator^=(const vec&u){this->insert(this->end(),u.begin(),u.end());return*this;} vec operator^(const vec&u)const{return vec{*this}^=u;} vec&operator+=(const vec&u){vec&v=*this;fo(i,v.size())v[i]+=u[i];return v;} vec&operator-=(const vec&u){vec&v=*this;fo(i,v.size())v[i]-=u[i];return v;} vec operator+(const vec&u)const{return vec{*this}+=u;} vec operator-(const vec&u)const{return vec{*this}-=u;} vec&operator++(){fe(*this,e)++e;return*this;} vec&operator--(){fe(*this,e)--e;return*this;} vec operator-()const{vec v=*this;fe(v,e)e=-e;return v;} ll size()const{return vector::size();} auto scan(const auto&f)const{pair,bool>r{};fe(*this,e)if constexpr(!vectorial)r.b?f(r.a,e),r:r={e,1};else if(auto s=e.scan(f);s.b)r.b?f(r.a,s.a),r:r=s;return r;} auto max()const{return scan([](auto&a,const auto&b){a)fe(v,e)e=e.zeta();fo(i,v.size()-1)v[i+1]+=v[i];return v;} }; templatestruct tensor_helper{using type=vec::type>;}; templatestruct tensor_helper<0,T>{using type=T;}; templateusing tensor=typename tensor_helper::type; templaterequires(sizeof...(A)>=2)vec(A...a)->vec(declval>()))>>>; vec(ll)->vec; void lin(auto&...a){(cin>>...>>a);} templatevoid pp(const auto&...a){ll n=sizeof...(a);((cout<0,c)),...);cout<struct linear_sieve{ ll n; veclpf; veclpf_ord; veclpf_pow; veclpf_pow_except; vecprimes; linear_sieve(ll n):n(n){ lpf.resize(n+1,-1); lpf_ord.resize(n+1); lpf_pow.resize(n+1); lpf_pow_except.resize(n+1); lpf[1]=lpf_ord[1]=lpf_pow[1]=lpf_pow_except[1]=1; fo(i,2,n+1){ if(lpf[i]==-1)primes.eb(lpf[i]=i); fe(primes,p){ if(p*i>n||p>lpf[i])break; lpf[p*i]=p; } int j=i/lpf[i]; lpf_ord[i]=lpf_ord[j]*(lpf[i]==lpf[j])+1; lpf_pow[i]=((lpf_pow[j]-1)*(lpf[i]==lpf[j])+1)*lpf[i]; lpf_pow_except[i]=i/lpf_pow[i]; } } auto multiplicative_function_enumerate(const auto&f)const{ vecr(n+1); r[1]=1; fo(i,2,n+1)r[i]=f(lpf[i],lpf_ord[i],lpf_pow[i])*r[lpf_pow_except[i]]; return r; } auto totient_enumerate()const{return multiplicative_function_enumerate(totient_prime_pow);} }; single_testcase void solve(){ LL(T); auto tot_sum=linear_sieve(1e7).totient_enumerate().zeta(); fo(T){ LL(N); ll s=tot_sum[N]-1; ll t=N*(N-1)/2-s; pp(s+t*2); } }}