传送门

题意：

$n\le 5e5$

思路：

首先有个显然的结论：当往集合中加入一个数$x$的时候，如果存在$d|x$且$d$不在集合中，那么加入$d$一定比加入$x$更优。
也就是说当我们加入$x$的时候，$x$的真因子一定都在集合中，那么我们对$[1,n]$求每个数求最大真因子是多少，让后排个序输出即可。

// Problem: F. Kate and imperfection
// Contest: Codeforces - Codeforces Round #632 (Div. 2)
// URL: https://codeforces.com/contest/1333/problem/F
// Memory Limit: 256 MB
// Time Limit: 1000 ms
// 
// Powered by CP Editor (https://cpeditor.org)//#pragma GCC optimize("Ofast,no-stack-protector,unroll-loops,fast-math")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,avx,avx2,popcnt,tune=native")
//#pragma GCC optimize(2)
#include<cstdio>
#include<iostream>
#include<string>
#include<cstring>
#include<map>
#include<cmath>
#include<cctype>
#include<vector>
#include<set>
#include<queue>
#include<algorithm>
#include<sstream>
#include<ctime>
#include<cstdlib>
#define X first
#define Y second
#define L (u<<1)
#define R (u<<1|1)
#define pb push_back
#define mk make_pair
#define Mid (tr[u].l+tr[u].r>>1)
#define Len(u) (tr[u].r-tr[u].l+1)
#define random(a,b) ((a)+rand()%((b)-(a)+1))
#define db puts("---")
using namespace std;//void rd_cre() { freopen("d://dp//data.txt","w",stdout); srand(time(NULL)); }
//void rd_ac() { freopen("d://dp//data.txt","r",stdin); freopen("d://dp//AC.txt","w",stdout); }
//void rd_wa() { freopen("d://dp//data.txt","r",stdin); freopen("d://dp//WA.txt","w",stdout); }typedef long long LL;
typedef unsigned long long ULL;
typedef pair<int,int> PII;const int N=1000010,mod=1e9+7,INF=0x3f3f3f3f;
const double eps=1e-6;int n;
int nt[N],prime[N],tot;
int cnt[N],ans[N];
bool st[N];void get_prime(int n) {for(int i=1;i<=n;i++) nt[i]=i;for(int i=2;i<=n;i++) {if(!st[i]) prime[++tot]=i;for(int j=i+i;j<=n;j+=i) st[j]=true,nt[j]=min(nt[j],i);}
}int main()
{
//	ios::sync_with_stdio(false);
//	cin.tie(0);cin>>n;get_prime(n+10);for(int i=1;i<=n;i++) nt[i]=i/nt[i];sort(nt+1,nt+1+n);for(int i=2;i<=n;i++) printf("%d ",nt[i]);return 0;
}
/**/