Atcoder AGC038 C- LCMs

$Description$
We have an integer sequence of length $N:A_0,A_1,\cdots,A_{N-1}$
Find the following sum:

$\sum_{i=0}^{N-2} \sum_{j=i+1}^{N-1} \mathrm{lcm}(A_i,A_j)$

$Solution$
图片说明

$Code$

#include<bits/stdc++.h>
using namespace std;
const int N=1e6+5;
const int p=998244353;
typedef long long ll;
int n,a[N],f[N]={0};
short int mu[N];
ll inv[N],w[N];
int main(){
    mu[1]=1;inv[1]=1;
    for(int i=2;i<N;i++)inv[i]=(p-p/i)*inv[p%i]%p;
    for(int i=1;i<N;i++)
    for(int j=i+i;j<N;j+=i)mu[j]-=mu[i];
    for(int i=1;i<N;i++)
    for(int j=i;j<N;j+=i)w[j]+=mu[j/i]*inv[i],w[j]=(w[j]%p+p)%p;
    cin>>n;
    for(int i=1;i<=n;i++)scanf("%d",&a[i]),f[a[i]]++;
    ll ans=0;
    for(int d=1;d<N;d++){
        ll res=0,ret=0;
        for(int i=d;i<N;i+=d){
            if(f[i]){
                ret+=1LL*i*((res*f[i]%p+1LL*f[i]*(f[i]-1)/2%p*i%p)%p)%p;
                res+=1LL*i*f[i]%p;
                ret%=p,res%=p;
            }
        }
        ans+=w[d]*ret%p;
        ans%=p;
    }
    printf("%lld\n",ans);
}