A number is called Harshad if it is divisible by the sum of its digits.
For example 102 is divisible by 3.
This quotient is not Harshad because 34 is not divisible by 7.
108 is a Multiple Harshad Number because the process ends at 1:
108/9=12; 12/3=4; 4/4=1.

Find the Multiple Harshad Numbers below 1000.

Hard bonus: Apparently there are only 15095 of these numbers. Can you prove the list is finite?

(In reply to re: part one by armando)

Indeed a program just checked the first 13244 numbers from the OEIS list and found no number beyond 84 that was not a multiple of 9. I'd suspect it would continue that to the end if it had not run into overflow at that point in the list.

Posted by Charlie on 2016-07-10 15:00:45