Harshad Numbers

Today I turned 24786 days old and one of the occurrences of this number in the OEIS was in A097569: right-truncatable Harshad numbers (zeros not permitted). Of course, I needed to ask myself the inevitable question: what is a Harshad number? Here is what Wikipedia had to say about it:

In recreational 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. Harshad numbers in base $\displaystyle n$ are also known as $\displaystyle n$-harshad (or $\displaystyle n$-Niven) numbers. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver. The term “Niven number” arose from a paper delivered by Ivan M. Niven at a conference on number theory in 1977. 

Stated mathematically, let $\displaystyle X$ be a positive integer with $\displaystyle m$ digits when written in base $\displaystyle n$, and let the digits be $\displaystyle a_{i}$ ( $\displaystyle i$ = 0, 1, ..., $\displaystyle m$ − 1). (It follows that $\displaystyle a_{i}$ must be either zero or a positive integer up to $\displaystyle n$ − 1.) $\displaystyle X$ can be expressed as $$\displaystyle X=\sum _{i=0}^{m-1}a_{i}n^{i}$$
If there exists an integer $\displaystyle A$ such that the following holds, then $\displaystyle X$ is a harshad number in base $\displaystyle n$: $$\displaystyle X=A\sum _{i=0}^{m-1}a_{i}$$ A number which is a harshad number in every number base is called an all-harshad number, or an all-Niven number. There are only four all-harshad numbers: 1, 2, 4, and 6 (The number 12 is a harshad number in all bases except octal).

So, getting back to 24786, it can be seen that it is a Harshad number because 2+4+7+8+6 = 27 and 24786/27 = 918. Truncating the last digit on the right gives 2478, so that 2+4+7+8 = 21 and 2478/21 = 118. Truncating again gives 247, so that 2+4+7 = 13 and 247/13 = 19. Truncating again gives 24, so that 2+4=6 and 24/6=4. Finally, 2 itself is of course a Harshad number.

Furthermore, it is asserted in the OEIS entry that 24786 is the final such number in the sequence of right-truncatable Harshad numbers. The full sequence is then given by:

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 18, 21, 24, 27, 36, 42, 45, 48, 54, 63, 72, 81, 84, 126, 216, 243, 247, 364, 423, 481, 486, 846, 2478, 8463, 24786