Perl 6, 47 bytes

{(0..$_**$_).grep: !*.polymod($_ xx*).repeated}

Returns a Seq. ( Seq is a basic Iterable wrapper for Iterators )

With an input of 16 it takes 20 seconds to calculate the 53905th element of the Seq (87887).

Expanded:

{       # bare block lambda with implicit parameter ｢$_｣

  ( 0 .. ($_ ** $_) )    # Range of values to be tested

  .grep:                 # return only those values

    !\                   # Where the following isn't true
    *\                   # the value
    .polymod( $_ xx * )  # when put into the base being tested
    .repeated            # has repeated values
  }
}