34 (number)

34 (number)
34
Cardinal thirty-four
Ordinal 34th
(thirty-fourth)
Factorization  2 \cdot 17
Divisors 1, 2, 17, 34
Roman numeral XXXIV
Binary 1000102
Octal 428
Duodecimal 2A12
Hexadecimal 2216

34 (thirty-four) is the natural number following 33 and preceding 35.

Contents

In mathematics

34 is the ninth distinct semiprime and has four divisors including unity and itself. Its neighbors, 33 and 35 also are distinct semiprimes having four divisors each, and 34 is the smallest number to be surrounded by numbers with the same number of divisors as it has. It is also in the first cluster of three distinct semiprimes, being within 33,34,35; the next such cluster of semiprimes is 85,86,87.

It is the ninth Fibonacci number and a companion Pell number. Since it is an odd-indexed Fibonacci number, 34 is a Markov number, appearing in solutions with other Fibonacci numbers, such as (1, 13, 34), (1, 34, 89), etc.

This number is the magic constant of a 4 by 4 normal magic square:[1]

MagicSquare-AlbrechtDürer.png

Thirty-four is a heptagonal number.

It has the aliquot sum, 20, in the following descending sequence 34,20,22,14,10,8,7,1. and it is the 6th composite member of the 7-aliquot tree.

There is no solution to the equation φ(x) = 34, making 34 a nontotient. Nor is there a solution to the equation x - φ(x) = 34, making 34 a noncototient.

In science

In sports

In other fields

34 is also:

Historical years

34 A.D., 34 B.C., 1934, 2034, etc.

References

  1. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 53. ISBN 978-1-84800-000-1. 
  2. ^ "Internet rules and laws: the top 10, from Godwin to Poe". The Daily Telegraph. 2009-10-23. http://www.telegraph.co.uk/technology/news/6408927/Internet-rules-and-laws-the-top-10-from-Godwin-to-Poe.html. Retrieved 2010-11-12. 
  3. ^ Grossman, Lev (July 18, 2011). "The Boy Who Lived Forever". Time 178 (3): 50. 
  4. ^ http://www.antipope.org/charlie/blog-static/2010/08/apropos-nothing.html
  5. ^ http://www.amazon.com/Rule-34-Charles-Stross/dp/0441020348/

External links


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