Harshad number

A Harshad number is an integer which is the multiple of the sum of its digits. For example, 27 is a Harshad number, as the sum of the digits of 27 is 9 and 27 is a multiple of 9.

Not all multiples of Harshad numbers are Harshad numbers.

48 is a Harshad number, but 96, which is a multiple of 48, is not.

Examples
The first 30 Harshad numbers are:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81.

Mathematical properties
Only 2, 3, 5 and 7 are the prime Harshad numbers.

All powers of 10, trivially, are Harshad numbers. This can be proven by seeing that 10n can be divisible by the sum of its digits, which is 1. This is the same for $$m\times10^n$$, where m is a Harshad number.