Zuckerman number

From Wikipedia, the free encyclopedia

You have new messages (last change).

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 dx (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).

[edit] Reference

  • J. J. Tattersall, Elementary number theory in nine chapters, p. 86. Cambridge: Cambridge University Press (2005)
This number theory-related article is a stub. You can help Wikipedia by expanding it.
Retrieved from "http://en.wikipedia.org../../../z/u/c/Zuckerman_number.html"