rough number

A k-rough numberMathworldPlanetmath is an integer n having only prime factorsMathworldPlanetmath greater than or equal to k. A number that is k-rough is thus not a k-smooth number. However, a prime p is both p-smooth and p-rough because neither inequality is strict.

For example, 771166905830363 is 7-rough since, in addition to having 7 as a prime factor, it has greater primes as factors. By comparison, 93386641873154605056 is not 7-rough, and is in fact 7-smooth, since all its divisorsMathworldPlanetmathPlanetmath are 2, 3, and powers of those small primes.

Title rough number
Canonical name RoughNumber
Date of creation 2013-03-22 18:09:46
Last modified on 2013-03-22 18:09:46
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 7
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A51
Related topic SmoothNumber