Niven numbers

Niven numbers (also called Harshad numbers or multidigital numbers) are positive integers divisible by the sum of their digits in base 10.

The first 20 Niven numbers are 1 2 3 4 5 6 7 8 9 10 12 18 20 21 24 27 30 36 40 42.

For any natural number n>0, one may also define n-Niven numbers to be those positive integers which are divisible by the sum of their digits in base n.

Trivially, the numbers up to n-1 are n-Niven numbers (since they are single-digit, the sum of digits is themselves), and n is an n-Niven number (since n in base n is always 10). Likewise an n-Niven number multiplied by n is an n-Niven number (since this just adds a 0 to the end of the number).

The Niven numbers may have been named after Larry Niven.

See also: Number theory