ClearAll[DisariumQ]
DisariumQ[n_Integer] := Module[{digs},
  digs = IntegerDigits[n];
  digs = digs^Range[Length[digs]];
  Total[digs] == n
]
i = 0;
Reap[Do[
   If[DisariumQ[n],
    i++;
    Sow[n]
    ];
   If[i == 19, Break[]]
   ,
   {n, 0, \[Infinity]}
   ]][[2, 1]]