170 (number)

Template:Refimprove Template:Infobox number 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.Script error: No such module "Unsubst".

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]