A Moran number is a special kind of [[harshad]] (Niven) number: not only is it divisible by its digit sum, but the quotient is prime. Take 42: its digits sum to 6, and 42 ÷ 6 = 7, which is prime — so 42 is a Moran number. The sequence: 18, 21, 27, 42, 45, 63, 84, 111, 114, 117, 133, 152.
Moran numbers are a strict subset of the Harshad numbers and are named in the recreational-mathematics literature; they're a nice example of layering one divisibility condition on top of another.