170 (number): Difference between revisions

← 169 170 171 →
← 170 171 172 173 174 175 176 177 178 179 → List of numbers; Integers; ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred seventy
Ordinal	170th; (one hundred seventieth)
Factorization	2 × 5 × 17
Divisors	1, 2, 5, 10, 17, 34, 85, 170
Greek numeral	ΡΟ´
Roman numeral	CLXX
Binary	101010102
Ternary	200223
Senary	4426
Octal	2528
Duodecimal	12212
Hexadecimal	AA16

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170 (one hundred [and] seventy) is the natural number following 169 and preceding 171.

In mathematics

170 is the smallest n for which φ(n) and σ(n) are both square (64 and 324 respectively). But 170 is never a solution for φ(x), making it a nontotient. Nor is it ever a solution to x - φ(x), making it a noncototient.

170 is a repdigit in base 4 (2222) and base 16 (AA), as well as in bases 33, 84, and 169. It is also a sphenic number.

170 is the largest integer for which its factorial can be stored in IEEE 754 double-precision floating-point format. This is probably why it is also the largest factorial that Google's built-in calculator will calculate, returning the answer as 170! = 7.25741562 × 10³⁰⁶.^{[citation needed]}

There are 170 different cyclic Gilbreath permutations on 12 elements,^[1] and therefore there are 170 different real periodic points of order 12 on the Mandelbrot set.^[2]

References

^ Sloane, N. J. A. (ed.). "Sequence A000048". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Diaconis, Persi; Graham, Ron (2012), "Chapter 5: From the Gilbreath Principle to the Mandelbrot Set", Magical Mathematics: the mathematical ideas that animate great magic tricks, Princeton University Press, pp. 61–83.

External links

[1] Sloane, N. J. A. (ed.). "Sequence A000048". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[2] Diaconis, Persi; Graham, Ron (2012), "Chapter 5: From the Gilbreath Principle to the Mandelbrot Set", Magical Mathematics: the mathematical ideas that animate great magic tricks, Princeton University Press, pp. 61–83.

[1]

[2]

@@ Line 8: / Line 8: @@
 ==In mathematics==
-is the smallest ''n'' for which φ(''n'') and σ(''n'') are both square(64 and 324 respectively). But 170 is never a solution for φ(''x''), making it a [[nontotient]]. Nor is it ever a solution to ''x'' - φ(''x''), making it a [[noncototient]].
+is the smallest ''n'' for which φ(''n'') and σ(''n'') are both square (64 and 324 respectively). But 170 is never a solution for φ(''x''), making it a [[nontotient]]. Nor is it ever a solution to ''x'' - φ(''x''), making it a [[noncototient]].
 is a [[repdigit]] in [[base 4]] (2222) and [[base 16]] (AA), as well as in bases 33, 84, and 169. It is also a [[sphenic number]].
-is the largest integer for which its [[factorial]] can be stored in [[double-precision floating-point format]]. This is probably why it is also the largest [[factorial]] that [[Google]]'s built-in [[calculator]] will calculate, returning the answer as 170! = 7.25741562 × 10<sup>306</sup>.
+is the largest integer for which its [[factorial]] can be stored in [[Double-precision_floating-point_format#IEEE_754_double-precision_binary_floating-point_format:_binary64|IEEE 754 double-precision floating-point format]]. This is probably why it is also the largest [[factorial]] that [[Google]]'s built-in [[calculator]] will calculate, returning the answer as 170! = 7.25741562 × 10<sup>306</sup>.{{Citation needed|date=April 2021}}
-There are 170 different [[cyclic permutation|cyclic]] [[Gilbreath permutation]]s on 12 elements,<ref>{{SloanesRef |sequencenumber=A000048}}</ref> and therefore there are 170 different [[real number|real]] periodic points of order 12 on the [[Mandelbrot set]].<ref>{{citation|title=Magical Mathematics: the mathematical ideas that animate great magic tricks|first1=Persi|last1=Diaconis|author1-link=Persi Diaconis|first2=Ron|last2=Graham|author2-link=Ronald Graham (mathematician)|publisher=Princeton University Press|year=2012|chapter=Chapter 5: From the Gilbreath Principle to the Mandelbrot Set|pages=61–83}}.</ref>
+There are 170 different [[cyclic permutation|cyclic]] [[Gilbreath permutation]]s on 12 elements,<ref>{{Cite OEIS|sequencenumber=A000048}}</ref> and therefore there are 170 different [[real number|real]] periodic points of order 12 on the [[Mandelbrot set]].<ref>{{citation|title=Magical Mathematics: the mathematical ideas that animate great magic tricks|first1=Persi|last1=Diaconis|author1-link=Persi Diaconis|first2=Ron|last2=Graham|author2-link=Ronald Graham (mathematician)|publisher=Princeton University Press|year=2012|chapter=Chapter 5: From the Gilbreath Principle to the Mandelbrot Set|pages=61–83}}.</ref>
-==In sports==
-* 170 is the maximum check-out possible in a standard game of [[darts]] (where the final score must be a double). It consists of two treble-twenties and a double-bullseye.<ref>{{citation|title=The Caddie Was a Reindeer: And Other Tales of Extreme Recreation|first=Steve|last=Rushin|publisher=Grove Press|year=2007|isbn=9781555847333|page=79|url=http://books.google.com/books?id=6mSlZuuQ6lIC&pg=PA79}}.</ref>
 ==See also==
@@ Line 32: / Line 29: @@
 ==External links==
-{{Commons cat|170 (number)}}
+{{Commons cat}}
 * [http://www.numdic.com/170 The Number 170]
-* [http://athensohio.net/reference/number/170/ Number Facts and Trivia: 170]
+* [https://web.archive.org/web/20091023061038/http://athensohio.net/reference/number/170/ Number Facts and Trivia: 170]
 * [http://www.positiveintegers.org/170 The Positive Integer 170]
 * [http://primes.utm.edu/curios/page.php/170.html Prime curiosities: 170]
-* [http://www.bcbuildingtrades.org/pages/careers_plumbers170.htm Plumbers and Pipefitters Union 170, Vancouver, BC]
-* [http://www.teamsterlocal170.com Teamsters Local 170, Worcester, MA]
-* [http://www.uelocal170.org/ West Virginia Public Workers Union Local 170]
 {{Integers|1}}