This may be confusing. An example:
12
1+2=3
3 is a factor of 12.
135
1+3+5=9
9 is a factor of 135.
555
5+5+5=15
15 is a factor of 555.
What is the name of this classification system or did I create a new one?
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This looks related to the fact that a number (in base 10) is a multiple of 3 if and only if the sum of its digits is a multiple of 3. Have you found any examples that are not multiples of 3? – Brian Hopkins Dec 05 '22 at 19:31
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1What makes this a "classification system"? – Hagen von Eitzen Dec 05 '22 at 19:56
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@HagenvonEitzen I didn't know the right term. Kind of like prime, parity, Fibonacci, that stuff. Also, It seems that it's either 3 or 7 that works. – Sumaesioso Dec 05 '22 at 20:00
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1@BrianHopkins It is easy to find examples that ar not multiples of 3. Try 476 or 999796 – Hagen von Eitzen Dec 05 '22 at 20:01
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I still need to know the name of this if it exists. – Sumaesioso Dec 05 '22 at 20:05
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These are called Harshad Numbers (or Niven numbers).
In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that base.
Jair Taylor
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1Nice to know. Here's the OEIS entry A005349 with several references. There's an interesting subsequence called the Moran numbers A001101 where the number divided by the sum of its digits is prime. – Brian Hopkins Dec 05 '22 at 20:48
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@BrianHopkins Thanks. Actually OEIS was how I found the name, but I forgot to include that link. – Jair Taylor Dec 05 '22 at 21:18
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