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Multiple Harshad Numbers (Posted on 2016-07-10) Difficulty: 3 of 5
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?

No Solution Yet Submitted by Jer    
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re(3): Moby Dick has been captured -- part 2 solved Comment 12 of 12 |
(In reply to re(2): Moby Dick has been captured -- part 2 solved by Charlie)

By the way, this agrees with


https://oeis.org/A236295/b236295.txt

showing the largest number of steps needed as 440, and there are 4 that need this many steps.

  Posted by Charlie on 2016-07-14 15:10:48
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