34 (number)

From Infogalactic: the planetary knowledge core
Jump to: navigation, search
33 34 35
Cardinal thirty-four
Ordinal 34th
(thirty-fourth)
Factorization 2 × 17
Divisors 1, 2, 17, 34
Roman numeral XXXIV
Binary 1000102
Ternary 10213
Quaternary 2024
Quinary 1145
Senary 546
Octal 428
Duodecimal 2A12
Hexadecimal 2216
Vigesimal 1E20
Base 36 Y36

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

In mathematics

34 is the ninth distinct semiprime and has four divisors including one 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[1] and a companion Pell number.[2] 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:[3]

Thirty-four is a heptagonal number.[4]

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.[5] Nor is there a solution to the equation x − φ(x) = 34, making 34 a noncototient.[6]

In science

In sports

Transportation

In other fields

34 is also:

See also

Rule 34 (Internet meme)

References

  1. "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  2. "Sloane's A002203 : Companion Pell numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  3. Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 53. ISBN 978-1-84800-000-1.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  4. "Sloane's A000566 : Heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  5. "Sloane's A005277 : Nontotients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  6. "Sloane's A005278 : Noncototients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  7. "Evidence for a new nuclear 'magic number'" (Press release). Saitama, Japan: Riken. 2013-10-10. Retrieved 2013-10-14.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
  8. Lua error in Module:Citation/CS1/Identifiers at line 47: attempt to index field 'wikibase' (a nil value).

External links