Henry Ernest Dudeney/Puzzles and Curious Problems/83 - Three Different Digits/Solution/Proof 1

by : $83$

 * Three Different Digits

Proof
From, we have A072081, which provides us with all the numbers divisible by the square of the sum of their digits in base $10$:


 * $1, 10, 20, 50, 81, 100, 112, 162, 200, 243, 324, 392, 400, 405, 500, 512, 605, 648, 810, 972, 1000, \ldots$

from which we pick up those required.