All Armstrong numbers calculator

Briefly, an Armstrong number  "is a number that is the sum of its own digits each raised to the power of the number of digits". For example `8208` is an Armstrong number because 8208 = 8^4 + 2^4 + 0^4 + 8^4. We will say that `8208` is a level-4 A-number and call the power sum of its digits, an aSum. Single digit numbers are obviously (level-1) Armstrong numbers , all the A-numbers up to level 4 are:

    1 2 3 4 5 6 7 8 9 
    153 370 371 407 
    1634 8208 9474

There is a finite number of A-numbers, this is because the magnitude of a number grows quicker then it's aSum so that after certain point, the aSum falls behind. The largest A-number is a level-39ner.
This code calculates all A-numbers up to level-39 with the following timings *:

  
  Level-15 0  sec.   41 numbers
  Level-18 2  sec.   46 numbers
  Level-20 6  sec.   51 numbers
  Level-21 11 sec.   53 numbers
  Level-22 15 sec    53 numbers
  Level-23 21 sec.   58 numbers
  Level-25 46 sec    66 numbers
  Level-39 3518 sec. (58 min) 88 numbers

* i7-4790K CPU @ 4.00GHz