F. Classical? （数论 + 思维 + 推理 + 容斥）

题目传送门

 题解1

题解2

#include <bits/stdc++.h>
#define LL long long
#define mem(i, j) memset(i, j, sizeof(i))
#define rep(i, j, k) for(int i = j; i <= k; i++)
#define dep(i, j, k) for(int i = k; i >= j; i--)
#define pb push_back
#define make make_pair
#define INF INT_MAX
#define inf LLONG_MAX
using namespace std;

template <typename T>
void read(T &x) {
    int s = 0, c = getchar();
    x = 0;
    while (isspace(c)) c = getchar();
    if (c == 45) s = 1, c = getchar();
    while (isdigit(c)) x = (x << 3) + (x << 1) + (c ^ 48), c = getchar();
    if (s) x = -x;
}

template <typename T>
void write(T x, char c = ' ') {
    int b[40], l = 0;
    if (x < 0) putchar(45), x = -x;
    while (x > 0) b[l++] = x % 10, x /= 10;
    if (!l) putchar(48);
    while (l) putchar(b[--l] | 48);
    putchar(c);
}

const int N=1e5+8;

bool sign[N];

int n,ma,u[N],cnt[N];

LL ans = 1LL;

vector<int> d[N];

stack<LL> s;

void pre(){
    for(int i=1;i<=ma;++i){
        for(int j=i;j<=ma;j+=i) d[j].push_back(i);
        if (i==1) u[i]=1;
        else if (i/d[i][1]%d[i][1]==0) u[i]=0;
        else u[i]=-u[i/d[i][1]];
    }
}

int coprime(int x){
    int tmp=0;
    for(int i:d[x])
        tmp+=u[i]*cnt[i];
    return tmp;
}

void updata(int x,int val){
    for(int i:d[x])
        cnt[i]+=val;
}

int main(void) {
    //ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
//    freopen("input.txt", "r", stdin);
//    freopen("output.txt", "w", stdout);
    read(n);
    for(int a,i=1;i<=n;++i){
        read(a);
        sign[a]=true;
        ma=max(ma,a);
    }
    pre();
    for(int i=1;i<=ma;++i)
        for(int j=2;i*j<=ma;++j)
            sign[i]|=sign[i*j];
    for(int qwq,i=ma;i>=1;--i) {
        if (!sign[i]) continue;
        qwq=coprime(i);
        while(qwq){
            if (__gcd(s.top(),(LL)i)==1){
                ans=max(s.top()*(LL)i,ans);
                --qwq;
            }
            updata(s.top(),-1);
            s.pop();
        }
        updata(i,1);
        s.push((LL)i);
    }
    write(ans,'
');
    return 0;
}