Find all possible 3-digit positive perfect powers that are divisible by the sum of their respective digits.

The following candidates were extracted from OEIS  (A001597):

100, 121, 125, 128, 144, 169, 196, 216, 225, 243, 256, 289, 324, 343, 361, 400, 441, 484, 512, 529, 576, 625, 676, 729, 784, 841, 900, 961,

After visual inspection which included:

1. Erasing all odd numbers with even s.o.d.  + leaving all ending by 00 or having s.o.d.=9 .

2. Trying for divisibility few “potential” leftovers

we are left with:

100, 144, 216, 225, 243, 324, 400, 441, 512, 576, 900.

All of the above (except 512) are divisible by 9 or 100 or both.

Rem: The (somehow omitted) 216, was inserted following Charlie's comment.

Thanks, Charlie.

Edited on July 29, 2015, 10:20 am

Posted by Ady TZIDON on 2015-07-29 08:30:27