Zuckerman numbers

Zuckerman numbers are natural numbers that are divided by the product of their numbers ^[1] .

Content

1 Example
2 sequence
3 Properties
4 notes

Example

212 is the Zuckerman number, since

2\cdot 1\cdot 2=4

{\ displaystyle 2 \ cdot 1 \ cdot 2 = 4}

and

212\,\vdots \,4

{\ displaystyle 212 \, \ vdots \, 4}

.

Sequence

All integers from 1 to 9 are Zuckerman numbers. All numbers including zero are not Zuckerman numbers. The first few Zuckerman numbers, consisting of more than one digit, are 11, 12, 15, 24, 36, 111, 112, 115, 128, 132, 135, 144, 175, 212, 216, 224, 312, 315 , 384 ^[2] .

Properties

Zuckerman numbers cannot contain more than eight different digits (since such a number cannot simultaneously contain 5 and even digits). The smallest Zuckerman number containing eight different digits is 1196342784 ^[3] .

Notes

↑ James J. Tattersall. Elementary Number Theory in Nine Chapters . - Cambridge University Press, 2005-06-30. - S. 86. - 458 p. - ISBN 9780521850148 .
↑ sequence A007602 in OEIS
↑ Zuckerman numbers (unopened) . www.numbersaplenty.com. Date of appeal September 15, 2016.

[1] James J. Tattersall. Elementary Number Theory in Nine Chapters . - Cambridge University Press, 2005-06-30. - S. 86. - 458 p. - ISBN 9780521850148 .

[2] sequence A007602 in OEIS

[3] Zuckerman numbers (unopened) . www.numbersaplenty.com. Date of appeal September 15, 2016.