#include #if __has_include() #endif using namespace std; #define eb emplace_back #define LL(...) ll __VA_ARGS__;lin(__VA_ARGS__) #define FO(n) for(ll IJK=n;IJK-->0;) #define fo(i,...) for(auto[i,i##stop,i##step]=for_range(0,__VA_ARGS__);i(1,__VA_ARGS__);i>=i##stop;i+=i##step) #define fe(a,e,...) for(auto&&__VA_OPT__([)e __VA_OPT__(,__VA_ARGS__]):a) #define defpp templatevoid pp(const auto&...a){[[maybe_unused]]const char*c="";((o<(a...);} #define entry defpp void main();void main2();}int main(){my::io();my::main();}namespace my{ namespace my{ void io(){cin.tie(nullptr)->sync_with_stdio(0);cout<constexpr auto for_range(T s,T b){T a=0;if(s)swap(a,b);return array{a-s,b,1-s*2};} templateconstexpr auto for_range(T s,T a,T b,T c=1){return array{a-s,b,(1-s*2)*c};} void lin(auto&...a){(cin>>...>>a);} constexpr ui64 kth_root_floor(ui64 a,ll k){ if (k==1)return a; auto within=[&](ui32 x){ui64 t=1;FO(k)if(__builtin_mul_overflow(t,x,&t))return false;return t<=a;}; ui64 r=0; of(i,sizeof(ui32)*CHAR_BIT)if(within(r|(1u<using pack_back_t=tuple_element_t>; } namespace my{ templateconcept vectorial=is_base_of_v::value_type>,remove_cvref_t>; templatestruct vec; templatestruct hvec_helper{using type=vec::type>;}; templatestruct hvec_helper<0,T>{using type=T;}; templateusing hvec=hvec_helper::type; templatestruct vec:vector{ using vector::vector; ll size()const{return vector::size();} auto&emplace_back(auto&&...a){vector::emplace_back(std::forward(a)...);return*this;} vec zeta()const{vec v=*this;if constexpr(vectorial){ }fo(i,v.size()-1)v[i+1]+=v[i];return v;} }; templaterequires(sizeof...(A)>=2)vec(const A&...a)->vec>>; } namespace my{ ll totient_prime_pow(ll p,i8,ll pk){return(pk-pk/p);} templatestruct linear_sieve{ T n; veclpf; veclpf_ord; veclpf_pow; veclpf_pow_except; vecprimes; linear_sieve(T n):n(n),lpf(n+1,-1),lpf_ord(n+1),lpf_pow(n+1),lpf_pow_except(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);} }; } namespace my{entry void main(){ LL(N); auto Phi=linear_sieve(N).totient_enumerate().zeta(); ll ans=0; fo(g,1,N+1){ ans+=Phi[sqrt_floor(N/g)]-1; } pp(ans*2+N); }}