A Zuckerman number is divisible by the product of its digits. The number 36 has digit product 18? No — 3 × 6 = 18, and 36 ÷ 18 = 2 exactly, so 36 qualifies. Any number containing a 0 digit is excluded (the product would be zero).
Zuckerman numbers are the multiplicative cousin of the Harshad numbers (divisible by the sum of their digits). Numbers that are both Harshad and Zuckerman — like 1, 12, 24, 36, 111 — are doubly well-behaved with respect to their own digits.