Zuckerman number

Zuckerman number

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 OEIS|id=A007602.

References

* J. J. Tattersall, "Elementary number theory in nine chapters", p. 86. Cambridge: Cambridge University Press (2005)


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