Why are Harshad numbers interesting in mathematics? Which applications do they have?

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They are also called Niven numbers

In: Mathematics
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They’re “interesting” because they have a property which people have found interesting. Math is more than just what can be applied to the real world. In fact, many people prefer math that has no application to the real world.

Basically, they are divisible by the sum of their digits, which doesn’t appear to be very common. So finding and testing for them is a minor challenge people have found interesting.