170 (number)

December 2012 170 1, 2, 5, 10, 17, 34, 85, 170 170 (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.April 2021 There are 170 different cyclic Gilbreath permutations on 12 elements,A000048 and therefore there are 170 different real periodic points of order 12 on the Mandelbrot set.Magical Mathematics: the mathematical ideas that animate great magic tricks Persi Diaconis Persi Diaconis Ron Graham Ronald Graham (mathematician) Princeton University Press 2012 Chapter 5: From the Gilbreath Principle to the Mandelbrot Set 61–83. References External links The Number 170 Number Facts and Trivia: 170 The Positive Integer 170 Prime curiosities: 170 1 Category:Integers