Harshad Number
A Positive Integer which is Divisible by the sum of its Digits, also called aNiven Number (Kennedy et al. 1980). The first few are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, ...(Sloane's A005349). Grundman (1994) proved that there is no sequence of more than 20 consecutive Harshad numbers, and found thesmallest sequence of 20 consecutive Harshad numbers, each member of which has 44,363,342,786 digits.
Grundman (1994) defined an 
-Harshad (or -Niven) number to be aPositive Integer which is Divisible by the sum of its digits in base
. Cai (1996) showed thatfor 
or 3, there exists an infinite family of sequences of consecutive -Harshad numbers of length 
.
References
Cai, T. ``On 2-Niven Numbers and 3-Niven Numbers.'' Fib. Quart. 34, 118-120, 1996. Cooper, C. N. and Kennedy, R. E. ``Chebyshev's Inequality and Natural Density.'' Amer. Math. Monthly 96, 118-124, 1989. Cooper, C. N. and Kennedy, R. ``On Consecutive Niven Numbers.'' Fib. Quart. 21, 146-151, 1993. Grundman, H. G. ``Sequences of Consecutive Kennedy, R.; Goodman, R.; and Best, C. ``Mathematical Discovery and Niven Numbers.'' MATYC J. 14, 21-25, 1980. Sloane, N. J. A. SequenceA005349/M0481in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995. Vardi, I. ``Niven Numbers.'' §2.3 in Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, pp. 19 and 28-31, 1991.-Niven Numbers.'' Fib. Quart. 32, 174-175, 1994.
- Adjoint Curve
- Adjoint Matrix
- Adjoint Operator
- Adjugate Matrix
- Adjunction
- Adleman-Pomerance-Rumely Primality Test
- Adleman-Rumely Primality Test
- Admissible
- Adéle
- Adéle Group
- Affine Complex Plane
- Affine Connection
- Affine Equation
- Affine Geometry
- Affine Group
- Affine Hull
- Affine Plane
- Affine Scheme
- Affine Space
- Affine Transformation
- Affinity
- Affix
- Aggregate
- AGM
- Agnesi's Witch