// LUOGU_RID: 110890204
// LUOGU_RID: 110143181
// LUOGU_RID: 110111001
#pragma GCC optimize(1)
#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize("Ofast")
#pragma GCC optimize("inline")
#pragma GCC optimize("-fgcse")
#pragma GCC optimize("-fgcse-lm")
#pragma GCC optimize("-fipa-sra")
#pragma GCC optimize("-ftree-pre")
#pragma GCC optimize("-ftree-vrp")
#pragma GCC optimize("-fpeephole2")
#pragma GCC optimize("-ffast-math")
#pragma GCC optimize("-fsched-spec")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("-falign-jumps")
#pragma GCC optimize("-falign-loops")
#pragma GCC optimize("-falign-labels")
#pragma GCC optimize("-fdevirtualize")
#pragma GCC optimize("-fcaller-saves")
#pragma GCC optimize("-fcrossjumping")
#pragma GCC optimize("-fthread-jumps")
#pragma GCC optimize("-funroll-loops")
#pragma GCC optimize("-freorder-blocks")
#pragma GCC optimize("-fschedule-insns")
#pragma GCC optimize("inline-functions")
#pragma GCC optimize("-ftree-tail-merge")
#pragma GCC optimize("-fschedule-insns2")
#pragma GCC optimize("-fstrict-aliasing")
#pragma GCC optimize("-falign-functions")
#pragma GCC optimize("-fcse-follow-jumps")
#pragma GCC optimize("-fsched-interblock")
#pragma GCC optimize("-fpartial-inlining")
#pragma GCC optimize("no-stack-protector")
#pragma GCC optimize("-freorder-functions")
#pragma GCC optimize("-findirect-inlining")
#pragma GCC optimize("-fhoist-adjacent-loads")
#pragma GCC optimize("-frerun-cse-after-loop")
#pragma GCC optimize("inline-small-functions")
#pragma GCC optimize("-finline-small-functions")
#pragma GCC optimize("-ftree-switch-conversion")
#pragma GCC optimize("-foptimize-sibling-calls")
#pragma GCC optimize("-fexpensive-optimizations")
#pragma GCC optimize("inline-functions-called-once")
#pragma GCC optimize("-fdelete-null-pointer-checks")
#include <stdio.h>
#include <cmath>
#include <algorithm>
#define rep(i,l,r) for(i=l;i<=r;++i)
using namespace std;
/*
类似一个区间平方根还有区间和的题，phi(x) 暴力跳是 log 级别的，第一问暴力。
第二问，先 i->phi(i) 建边，然后 dfn 序，最后记录 dfn 最大最小直接 lca。
反正树高 log，暴力跳。
*/
const int sq=10000,V=5000005,N=100005,inf=2e9;
int nd[sq],tag[sq],md[sq],L[sq],R[sq],lsum[sq],npos[sq],mpos[sq];
int phi[V],p[V];
bool np[V];
int n;
int v[N],son[V],own[N],top[V],siz[V],dfn[V],fat[V],dep[V];
int head[V];
class edge
{
public:
	int go,nxt;
}e[V<<2];
int all,tot;
inline void add_edge(int x,int y)
{
	e[++all]={head[x],y};
	head[x]=all;
}
void dfs1(int id,int fa)
{
//	printf("%d %d\n",id,fa);
	int i,nxt;
	fat[id]=fa;
	dep[id]=dep[fa]+1;
	siz[id]=1;
	for(i=head[id];i;i=e[i].go)
	{
		nxt=e[i].nxt;
		if(nxt==fa)
			continue;
		dfs1(nxt,id);
		siz[id]+=siz[nxt];
		if(siz[nxt]>siz[son[id]])
			son[id]=nxt;
	}
//	printf("%d\n",id==son[id]);
	return ;
}
inline void dfs2(int id,int frm)
{
	int i,nxt;
//	printf("%d %d %d %d\n",id,son[id],dfn[id],frm);
	dfn[id]=++tot;
	top[id]=frm;
	if(son[id])
		dfs2(son[id],frm);
	for(i=head[id];i;i=e[i].go)
	{
		nxt=e[i].nxt;
		if(nxt==fat[id] || nxt==son[id])
			continue;
		dfs2(nxt,nxt);
	}
	return ;
}
inline int lca(int x,int y)
{
//	printf("%d %d no ",x,y);
	while(top[x]!=top[y])
	{
		if(dep[top[x]]<dep[top[y]])
			swap(x,y);
		x=fat[top[x]];
	}
//	puts("lca is ok");
	return dep[x]<dep[y]?x:y;
}
inline void solve(int id,int l,int r,int tag)
{
	if(tag==0 || lsum[id]==r-l+1)
		return ;
	register int i,j;
	rep(i,l,r)
		rep(j,1,tag)
		{
			lsum[id]=lsum[id]-dep[v[i]]+dep[phi[v[i]]];
			v[i]=phi[v[i]];
			if(v[i]==1)
				break;
		}
	rep(i,l,r)
	{
		nd[id]=min(nd[id],dfn[v[i]]);
		if(nd[id]==dfn[v[i]])
			npos[id]=i;
		md[id]=max(md[id],dfn[v[i]]);
		if(md[id]==dfn[v[i]])
			mpos[id]=i;
	}
	return ;
}
inline void work(int op,int l,int r)
{
	register int lcasum=0;
	register int i,j,id;
	if(op==1)
	{
		if(own[l]==own[r])
		{
			id=own[l];
			rep(i,l,r)
			{
				lsum[id]=lsum[id]-dep[v[i]]+dep[phi[v[i]]];
				v[i]=phi[v[i]];
				nd[id]=min(nd[id],dfn[v[i]]);
				if(nd[id]==dfn[v[i]])
					npos[id]=i;
				md[id]=max(md[id],dfn[v[i]]);
				if(md[id]==dfn[v[i]])
					mpos[id]=i;
			}
		}else
		{
			id=own[l];
			rep(i,l,R[own[l]])
			{
				lsum[id]=lsum[id]-dep[v[i]]+dep[phi[v[i]]];
				v[i]=phi[v[i]];
				nd[id]=min(nd[id],dfn[v[i]]);
				if(nd[id]==dfn[v[i]])
					npos[id]=i;
				md[id]=max(md[id],dfn[v[i]]);
				if(md[id]==dfn[v[i]])
					mpos[id]=i;
			}
			id=own[r];
			rep(i,L[own[r]],r)
			{
				lsum[id]=lsum[id]-dep[v[i]]+dep[phi[v[i]]];
				v[i]=phi[v[i]];
				nd[id]=min(nd[id],dfn[v[i]]);
				if(nd[id]==dfn[v[i]])
					npos[id]=i;
				md[id]=max(md[id],dfn[v[i]]);
				if(md[id]==dfn[v[i]])
					mpos[id]=i;
			}
			rep(i,own[l]+1,own[r]-1)
				++tag[i];
		}
	}else
	{
		int ndfn,xdfn,nid,xid;
		if(own[l]==own[r])
		{
			solve(own[l],L[own[l]],R[own[r]],tag[own[l]]);
			tag[own[l]]=0;
			ndfn=inf;
			xdfn=-inf;
			rep(i,l,r)
			{
				if(dfn[v[i]]<ndfn)
				{
					ndfn=dfn[v[i]];
					nid=v[i];
				}
				if(dfn[v[i]]>xdfn)
				{
					xdfn=dfn[v[i]];
					xid=v[i];
				}
				lcasum+=dep[v[i]];
			}
			printf("%d\n",lcasum-(r-l+1)*dep[lca(xid,nid)]);
		}else
		{
			ndfn=inf;
			xdfn=-inf;
			solve(own[l],L[own[l]],R[own[l]],tag[own[l]]);
			tag[own[l]]=0;
			rep(i,l,R[own[l]])
			{
				if(dfn[v[i]]<ndfn)
				{
					ndfn=dfn[v[i]];
					nid=v[i];
				}
				if(dfn[v[i]]>xdfn)
				{
					xdfn=dfn[v[i]];
					xid=v[i];
				}
				lcasum+=dep[v[i]];
			}
			rep(i,own[l]+1,own[r]-1)
			{
				solve(i,L[i],R[i],tag[i]);
				tag[i]=0;
				if(nd[i]<ndfn)
				{
					ndfn=nd[i];
					nid=v[npos[i]];
				}
				if(md[i]>xdfn)
				{
					xdfn=md[i];
					xid=v[mpos[i]];
				}
				lcasum+=lsum[i];
			}
			solve(own[r],L[own[r]],R[own[r]],tag[own[r]]);
			tag[own[r]]=0;
			rep(i,L[own[r]],r)
			{
				if(dfn[v[i]]<ndfn)
				{
					ndfn=dfn[v[i]];
					nid=v[i];
				}
				if(dfn[v[i]]>xdfn)
				{
					xdfn=dfn[v[i]];
					xid=v[i];
				}
				lcasum+=dep[v[i]];
			}
//			printf("%d %d\n",lcasum,lca(xid,nid));
			printf("%d\n",lcasum-(r-l+1)*dep[lca(xid,nid)]);
		}
	}
	return ;
}
inline void pre()
{
	register int i,j;
	register int cnt=0;
	phi[1]=1;
	rep(i,2,V-1)
	{
		if(!np[i])
			p[++cnt]=i,phi[i]=i-1;
		for(j=1;j<=cnt && 1ll*i*p[j]<V;++j)
		{
			np[i*p[j]]=1;
			if(i%p[j]==0)
			{
				phi[i*p[j]]=phi[i]*p[j];
				break;
			}
			else
				phi[i*p[j]]=phi[i]*phi[p[j]];
		}
	}
}
int main()
{
	int m,l,r;
	int i,j,opt,block,cnt;
	scanf("%d %d",&n,&m);
	rep(i,1,n)
		scanf("%d",v+i);
	pre();
	rep(i,2,V-1)
	{
		add_edge(phi[i],i);
	}
	dfs1(1,0);
	dfs2(1,1);
	cnt=n/(block=1500);
	rep(i,1,cnt)
	{
		L[i]=R[i-1]+1;
		R[i]=cnt*i;
	}
//	rep(i,1,10)printf("phi[%d]=%d,dep[%d]=%d\n",i,phi[i],i,dep[i]);
	if(R[cnt]<n)
	{
		++cnt;
		L[cnt]=R[cnt-1]+1;
		R[cnt]=n;
	}
	rep(i,1,cnt)
	{
		nd[i]=inf;
		md[i]=-inf;
		rep(j,L[i],R[i])
		{
			own[j]=i;
			nd[i]=min(nd[i],dfn[v[j]]);
			if(nd[i]==dfn[v[j]])
				npos[i]=j;
			md[i]=max(md[i],dfn[v[j]]);
			if(md[i]==dfn[v[j]])
				mpos[i]=j;
			lsum[i]+=dep[v[j]];
		}
	}
//	rep(i,1,n)
//		printf("%d %d %d %d\n",phi[i],i,top[i],fat[i]);
	while(m--)
	{
		scanf("%d %d %d",&opt,&l,&r);
		work(opt,l,r);
	}
	return 0;
}

码风有点混乱邪恶

大体的思路就是去均摊，但是不知道哪里假了一直 tle on #4