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Zuckerman number∗ CompositeFan† 2013-03-21 20:51:13 Consider the integer 384. Multiplying its digits, 3 × 8 × 4 = 96 and 384 = 91. 96 When an integer is divisible by the product of its digits, it’s called a Zuckerman number. That is, given m is the number of digits of n and dx (for x ≤ k) is an integer of n, m Y di |n i=1 All 1-digit numbers and the base number itself are Zuckerman numbers. It is possible for an integer to be divisible by its multiplicative digital root and yet not be a Zuckerman number because it doesn’t divide its first digit product evenly (for example, 1728 in base 10 has multiplicative digital root 2 but is not divisible by 1 × 7 × 2 × 8 = 112). The reverse is also possible (for example, 384 is divisible by 96, as shown above, but clearly not by its multiplicative digital root 0). References [1] J. J. Tattersall, Elementary number theory in nine chapters, p. 86. Cambridge: Cambridge University Press (2005) ∗ hZuckermanNumberi created: h2013-03-21i by: hCompositeFani version: h38134i Privacy setting: h1i hDefinitioni h11A63i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. 1