a[i]=sigma a[j] +fac[i]
j从1到i-1
fac:因子个数,比如4有1,2,4三个因子,如果有质因数p1,p2,p3,对应指数为a1,a2,a3,则fac[i]=(a1+1)*(a2+1)*(a3+1)
#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<stdlib.h>
#define max(a,b) a>b?a:b
#define min(a,b) a<b?a:b
#define mod 998244353
#define Maxn 1000009
using namespace std;
typedef long long ll;
ll a[999999],n,sum[Maxn];
int prime[Maxn];
int fac[Maxn],cnt[Maxn],cntt;
void ini()
{
for(int i=2;i<=Maxn;i++)
{
if(!prime[i])
{
prime[cntt++]=i;
fac[i]=2;//factor
cnt[i]=1;//
}
for(int j=0;j<cntt;j++){
if(prime[j]*i>Maxn)break;
prime[prime[j]*i]=1;
if(i%prime[j]==0)
{
fac[i*prime[j]]=fac[i]/(cnt[i]+1)*(cnt[i]+2);
cnt[i*prime[j]]=cnt[i]+1;
break;
}
else
{
fac[i*prime[j]]=fac[i]*fac[prime[j]];
cnt[i*prime[j]]=1;
}
}
}
return;
}
int i,j,k=1;
int main()
{
scanf("%lld",&n);
a[1]=1;
a[2]=3;
a[3]=6;
sum[1]=1;
sum[2]=4;
sum[3]=10;
ini();
for(int i=4;i<=n;i++)
{
a[i]+=sum[i-1]+fac[i]%mod;
sum[i]=sum[i-1]+a[i]%mod;
}
printf("%lld",a[n]%mod);
return 0;
}