#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);} 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...});} 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;} auto pop_back(){auto r=this->back();vector::pop_back();return r;} 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>>; templateauto iota(ll l,ll r=0){if(l>r)swap(l,r);vecv(r-l);std::iota(v.begin(),v.end(),l);return v;} } namespace my{ templateauto prime_enumerate(T n){ vecsieve(n/3+1,1); for(T p=5,d=4,i=1,rn=sqrt_floor(n);p<=rn;p+=d=6-d,i++){ if(!sieve[i])continue; for(T q=(p*p)/3,r=d*p/3+(d*p%3==2),s=p*2;qr{2,3}; for(T p=5,d=4,i=1;p<=n;p+=d=6-d,i++)if(sieve[i])r.eb(p); while(r.size()&&r.back()>n)r.pop_back(); return r; } } namespace my { templateauto interval_totient_enumerate(ll L,ll R){ auto remain=iota(L,R); auto res=iota(L,R); fe(prime_enumerate(sqrt_floor(R-1)),p){ fo(i,max(ceil(L,p)*p,p),R,p){ while(remain[i-L]%p==0)remain[i-L]/=p; res[i-L]-=res[i-L]/p; } } fo(i,L,R)if(remain[i-L]>1)res[i-L]-=res[i-L]/remain[i-L]; return res; } } namespace my{entry void main(){ LL(N); auto Phi=interval_totient_enumerate(0,N+1).zeta(); ll ans=0; fo(g,1,N+1)ans+=Phi[sqrt_floor(N/g)]-1; pp(ans*2+N); }}