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A base ${\displaystyle b}$ Harshad number is a positive integer that is divisible by the sum of its base ${\displaystyle b}$ digits. For example, in the decimal numeral system, 1729 is a Harshad number since 1 + 7 + 2 + 9 = 19, and 1729 = 19 × 91. Also called Niven numbers or, much less commonly, multidigital numbers.
It is important to note that the definition requires divisibility by the sum of digits, not the digital root. One could be led astray to think that all multiples of 9 are Harshad numbers in decimal, but 99 is not: 9 + 9 = 18, which is even, but 99 is odd. In general, many consecutive multiples of ${\displaystyle b-1}$ can be found to be Harshad numbers in base ${\displaystyle b}$.
Single digit numbers are trivially Harshad numbers, and in fact we can say that the only way for a positive prime number ${\displaystyle p}$ to be a Harshad number in base ${\displaystyle b}$ is for ${\displaystyle p\leq b}$ to hold true.
The following table shows first few Harshad numbers greater than ${\displaystyle b}$.
 ${\displaystyle b}$ Small Harshad numbers A-number 2 4, 6, 8, 10, 12, 16, 18, 20, 21, 24, 32, 34, 36, 40, 42, 48 A049445 3 4, 6, 8, 9, 10, 12, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32 A064150 4 6, 8, 9, 12, 16, 18, 20, 21, 24, 28, 30, 32, 33, 35, 36, 40, 42 A064438 5 6, 8, 10, 12, 15, 16, 18, 20, 24, 25, 26, 27, 28, 30, 32, 36 A064481 6 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 42, 44, 45, 48, 50, 55 7 8, 9, 12, 14, 15, 16, 18, 21, 24, 27, 28, 30, 32, 35, 36, 40, 42 8 14, 16, 21, 24, 28, 32, 35, 40, 42, 48, 49, 56, 64, 66, 70, 72 A245802 9 10, 12, 16, 18, 20, 24, 27, 28, 30, 32, 36, 40, 45, 48, 50, 54 10 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63 A005349 11 12, 15, 20, 22, 24, 25, 30, 33, 35, 36, 40, 44, 45, 48, 50, 55 12 22, 24, 33, 36, 44, 48, 55, 60, 66, 72, 77, 84, 88, 96, 99, 108
Only 1, 2, 4, 6 are Harshad numbers in every integer base ${\displaystyle b>1}$.