Encyclopedia > Niven numbers

Article Content

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).