#include<iostream>
#include<cstdio>
#include<set>
#include<vector>
#define N 2000000
#define M 8000000
#define g 3
#define mod 998244353
using namespace std;
int read()
{
    char c=0;
    int sum=0;
    while (c<'0'||c>'9') c=getchar();
    while ('0'<=c&&c<='9') sum=sum*10+c-'0',c=getchar();
    return sum;
}
int fast_pow(int a,int b)
{
    int res=1,mul=a;
    while (b)
    {
	if (b&1) res=1ll*res*mul%mod;
	mul=1ll*mul*mul%mod,b>>=1;
    }
    return res;
}
void Adder(int &x,int d)
{
    x+=d;
    if (x>=mod) x-=mod;
    return;
}
void Adder2(int &x,int d)
{
    x+=d;
    if (x<0) x+=mod;
    return;
}
int MD(int x)
{
    return x>=mod?x-mod:x;
}
int MD2(int x)
{
    return x<0?x+mod:x;
}
struct reads
{
    int num,data;
};
int n,rst=1,res,ans,inv[N+1],rev[M+1],r[N+1],maxn[N+1],cmaxn[N+1],cnt[N+1],dp[M+1],delta[M+1];
bool nprime[N+1];
vector<reads>p[N+1];
void NTT(int limit,int *s,int type)
{
    int s1,s2,d;
    for (int i=1;i<limit;++i) rev[i]=(rev[i>>1]>>1)|((i&1)?(limit>>1):0);
    for (int i=0;i<limit;++i)
	if (rev[i]>i)
	    swap(s[i],s[rev[i]]);
    for (int i=2,w;i<=limit;i<<=1)
    {
	if (type==1) w=fast_pow(g,(mod-1)/i);
	else w=fast_pow(g,(mod-1)/i*(i-1));
	for (int j=0;j+i-1<=limit;j+=i)
	    for (int k=j,wn=1;k<j+(i>>1);++k,wn=1ll*wn*w%mod)
		s1=s[k],s2=1ll*s[k+(i>>1)]*wn%mod,s[k]=MD(s1+s2),s[k+(i>>1)]=MD2(s1-s2);
    }
    if (type==-1)
    {
	d=fast_pow(limit,mod-2);
	for (int i=0;i<limit;++i) s[i]=1ll*s[i]*d%mod;
    }
    return;
}
int main()
{
    int res,limit=1,x,cst;
    inv[1]=1;
    for (int i=2;i<=N;++i) inv[i]=MD2(-1ll*(mod/i)*inv[mod%i]%mod);
    for (int i=2;i<=N;++i)
	if (!nprime[i])
	{
	    for (int j=(i<<1);j<=N;j+=i) nprime[j]=1;
	}
    for (int i=2;i<=N;++i)
	if (!nprime[i])
	    for (int j=i;j<=N;j+=i)
	    {
		x=j,cst=0;
		while (x%i==0) x/=i,cst++;
		p[j].push_back((reads){i,cst});
	    }
    n=read();
    for (int i=1;i<=n;++i)
    {
	r[i]=read();
	for (int j=0;j<p[r[i]].size();++j) maxn[p[r[i]][j].num]=max(maxn[p[r[i]][j].num],p[r[i]][j].data);
    }
    for (int i=1;i<=N;++i)
	for (int j=1;j<=maxn[i];++j)
	    rst=1ll*rst*i%mod;
    for (int i=1;i<=n;++i)
	for (int j=0;j<p[r[i]].size();++j)
	{
	    if (maxn[p[r[i]][j].num]==p[r[i]][j].data) cnt[p[r[i]][j].num]++;
            else cmaxn[p[r[i]][j].num]=max(cmaxn[p[r[i]][j].num],p[r[i]][j].data);
	}
    for (int i=1;i<=n;++i)
    {
	res=1;
	for (int j=0;j<p[r[i]].size();++j)
	    if (cnt[p[r[i]][j].num]==1&&maxn[p[r[i]][j].num]==p[r[i]][j].data)
		for (int k=1;k<=maxn[p[r[i]][j].num]-cmaxn[p[r[i]][j].num];++k)
		    res=1ll*res*inv[p[r[i]][j].num]%mod;
	Adder(dp[r[i]],res),Adder2(delta[r[i]+r[i]],-1ll*res*res%mod);
    }
    while (limit<=N) limit<<=1;
    NTT(limit,dp,1);
    for (int i=0;i<=limit;++i) dp[i]=1ll*dp[i]*dp[i]%mod;
    NTT(limit,dp,-1);
    for (int i=1;i<=N;++i) Adder(delta[i],dp[i]),delta[i]=1ll*delta[i]*inv[2]%mod;
    for (int i=1;i<=N;++i)
    {
	res=rst;
	for (int j=0;j<p[i].size();++j)
	    for (int k=1;k<=p[i][j].data-maxn[p[i][j].num];++k)
		res=1ll*res*p[i][j].num%mod;
	Adder(ans,1ll*delta[i]*res%mod);
    }
    printf("%d\n",ans);
    return 0;
}