Zuckerman number

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A Zuckerman number is an integer that is divisible by the product of its digits in a given number base. Or, to put it algebraically, given a positive integer n with m digits d_x (with x < m + 1) in base b, if it's true that

${\prod_{i = 1}^m d_i} \mid n$

then n is a Zuckerman number. All integers between 1 and the base number are Zuckerman numbers. No integer with a zero as one or more of its digits in base b can be a Zuckerman number in that base.

In base 10, the first few Zuckerman numbers with more than one digit are

11, 12, 15, 24, 36, 111, 112, 115, 128, 132, 135, 144, 175, 212, 216, 224, 312, 315, 384.

These are listed in (sequence A007602 in OEIS).