Harshad Number - Nivenmorphic Numbers

Nivenmorphic Numbers

A Nivenmorphic number or Harshadmorphic number for a given number base is an integer t such that there exists some Harshad number N whose digit sum is t, and t, written in that base, terminates N written in the same base.

For example, 18 is a Nivenmorphic number for base 10:

16218 is a Harshad number 16218 has 18 as digit sum 18 terminates 16218

Sandro Boscaro determined that for base 10 all positive integers are Nivenmorphic numbers except 11.

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