Definition:Niven Number

A Niven number (in a given number base $$b$$) is a positive integer which is divisible by the sum of its digits in that given base $b$.

That is, $$N$$ is a Niven number base $$b$$ iff:


 * $$\exists A \in \Z: N = \sum_{k=0}^m r_k b^k = A \sum_{k=0}^m r_k$$

where $$\sum_{k=0}^m r_k b^k$$ is the representation of $$N$$ as defined according to the Basis Representation Theorem.

Also see

 * Harshad Number
 * All-Harshad Number