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)


Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Zuckerman, Solly, Lord — (1904–93)    British scientist. A brilliant anatomist and zoologist, Cape Town born Zuckerman settled in England and first became known for his research on apes and monkeys. He served during the war as a scientific adviser to the RAF. In the post …   Who’s Who in Jewish History after the period of the Old Testament

  • number theory — Math. the study of integers and their relation to one another. Also called theory of numbers. [1910 15] * * * Branch of mathematics concerned with properties of and relations among integers. It is a popular subject among amateur mathematicians… …   Universalium

  • 132 (number) — Number|number = 132 cardinal = one hundred [and] thirty two ordinal = nd ordinal text = one hundred [and] thirty second numeral = factorization = 2^2 cdot 3 cdot 11 prime = divisor = 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 unicode = greek… …   Wikipedia

  • 135 (number) — Number|number = 135 range = 130s cardinal = one hundred [and] thirty five ordinal = th ordinal text = one hundredth [and] thirty fifth numeral = 135 factorization = 3^3 cdot 5 prime = divisor = 1, 3, 5, 9, 15, 27, 45, 135 roman = CXXXV unicode =… …   Wikipedia

  • 600 (number) — For the year 600, see 600 BC or 600 AD. ← 599 601 → 600 List of numbers Integers ← …   Wikipedia

  • 210 (number) — 210 is the natural number following 209 and preceding 211. In mathematics 210 is a composite number, an abundant number, and the product of the first four prime numbers (2, 3, 5, and 7), and thus a primorial. It is also the sum of eight… …   Wikipedia

  • 700 (number) — This article is about the numbers 700 through 799; for each individual number, see its section below. 700 (seven hundred) is the natural number following 699 and preceding 701. List of numbers Integers ← 0 100 200 300 400 500 600 700 800 …   Wikipedia

  • 800 (number) — This article is about the number 800. For the Common Era Year 800, see 800. For other uses, see 800 (disambiguation) 800 (eight hundred) is the natural number following 799 and preceding 801. List of numbers Integers ← 0 100 200 300 400 500 600… …   Wikipedia

  • 220 (number) — 220 ( two hundred [and] twenty ) is the natural number following 219 and preceding 221.In mathematicsIt is a composite number, with its divisors being 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, making it an amicable number with 284. [Bryan Bunch …   Wikipedia

  • Sum-product number — A sum product number is an integer that in a given base is equal to the sum of its digits times the product of its digits. Or, to put it algebraically, given an integer n that is l digits long in base b (with d x representing the x th digit), ifn …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”