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linear_sieve.cpp
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linear_sieve.cpp
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#include <iostream>
#include <vector>
#define sz(s) (int)s.size()
using namespace std;
const int nmm = 5e6+50;
int cnt[nmm],a[nmm];
long long dp[nmm];
vector<int>primes;
bool is_composite[nmm];
void linear_sieve() {
for(int i=0;i<nmm;i++) {
is_composite[i] = false;
}
for(int i=2;i<nmm;i++) {
if(!is_composite[i]) primes.push_back(i);
for(int j=0;j<sz(primes) and primes[j]*i<nmm;j++) {
is_composite[i*primes[j]] = true;
if(i%primes[j]==0) break;
}
}
}
long long max(long long x,long long y) {
if(x > y) return x;
return y;
}
void solve() {
int n;
cin>>n;
for(int i=0;i<n;i++) {
int x;
cin>>x;
a[x]++;
}
for(int i=2;i<=nmm;i++) {
for(int j=i;j<nmm;j+=i) {
cnt[i] += a[j];
}
}
for(long long int i=nmm-10;i>1;i--) {
dp[i] = cnt[i]*i;
for(auto u:primes) {
if(u*i>=nmm) break;
dp[i] = max(dp[i],dp[i*u]+i*(cnt[i]-cnt[i*u]));
}
}
long long int ans = 0;
for(long long int i=nmm-1;i>1;i--) {
ans = max(ans,dp[i]+n-cnt[i]);
}
cout<<ans<<"\n";
}
signed main() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);cout.tie(nullptr);
linear_sieve();
int testcases=1;
//cin>>testcases;
while(testcases--) solve();
return 0;
}