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 Moby Dick has been captured -- part 2 solved by Charlie)

Thar she blows!  You're one up on Ahab.

I plan to share some of this with some 6th graders. Is it possible to generate the full string of either the largest MHD or the one with the most steps. 

On second thought how many pages would it take to print this out? I may just share the largest MHN, which the OEIS lists.

Edited on July 14, 2016, 1:57 pm

Posted by Jer on 2016-07-14 13:55:58