fcn classify(k){
   const MAX=(2).pow(47);  // 140737488355328
   ak,aks:=aliquot(k), ak.walk(16);
   _,a2,a3:=aks;
   if(a2==k) return("perfect");
   if(a3==k) return("amicable");
   aspiring:='wrap(){
      foreach n in (aks.len()-1){ if(aks[n]==aks[n+1]) return(True) }
      False
   };
   cyclic:='wrap(){
      foreach n in (aks.len()-1){ if(aks[n+1,*].holds(aks[n])) return(aks[n]) }
      False
   };
   (if(aks.filter1('==(0))!=False) "terminating"
    else if(n:=aks[1,*].filter1n('==(k))) "sociable of length " + (n+1)
    else if(aks.filter1('>(MAX)))  "non-terminating"
    else if(aspiring())            "aspiring"
    else if((c:=cyclic())!=False)  "cyclic on " + c
    else                           "non-terminating" )
   + " " + aks.filter();
}