A Harshad number is a positive integer which is divisible by the sum of its digits,
also called a Niven number (Kennedy et al. 1980) or a multidigital number
(Kaprekar 1955). The first few are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21,
24, ... (OEIS A005349). Grundman (1994) proved
that there is no sequence of more than 20 consecutive Harshad numbers, and found
the smallest sequence of 20 consecutive Harshad numbers, each member of which has
digits.
Grundman (1994) defined an 
-Harshad (or 
-Niven) number to be a positive
integer which is divisible by the sum of its digits
in base 
.
Cai (1996) showed that for 
or 3, there exists an infinite family of sequences of consecutive
-Harshad numbers of length 
.
Define an all-Harshad (or all-Niven) number as a positive integer which is divisible by the sum of its digits in all bases 
. Then only 1, 2, 4, and 6 are all-Harshad numbers.
-Niven Numbers." Fib. Quart. 32, 174-175,
1994.Kaprekar, D. R. "Multidigital Numbers." Scripta
Math. 21, 27, 1955.Kennedy, R. E. and Cooper, C. N.
"On the Natural Density of the Niven Numbers." Abstract 816-11-219, Abstracts
Amer. Math. Soc. 6, 17, 1985.Kennedy, R.; Goodman, R.; and
Best, C. "Mathematical Discovery and Niven Numbers." MATYC J. 14,
21-25, 1980.Sloane, N. J. A. Sequence