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 Multiple Harshad Numbers (Posted on 2016-07-10)
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 No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: part one | Comment 2 of 12 |
(In reply to part one by Charlie)

As it could be expected most are multiples of 9.

In a quick check I see that among the first 90 numbers, the highest which is not a 9 multiple is 84.

But it is only a two steps number as all the lowers
84/12=7
7/7=1

 Posted by armando on 2016-07-10 13:06:21

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