public class NextSmoothNumber
extends Object

A class to determine the next k-smooth number (i.e. a number divisible only by prime numbers up to k), given a lower bound n. Based on A. Granville, Smooth numbers: computational number theory and beyond:

5.7. Finding smooth numbers computationally. The obvious way to find y-smooth numbers in (x; x + z) with z ≤ x is to initialize an array a[i] := 0 for 1 ≤ i ≤ z (where a[i] corresponds to x + i). For each successively larger prime power p^j ≤ x + z with p ≤ y, determine the smallest i such that p^j divides x + i and then add log(p) to a[i], a[i + p^j], a[i + 2p^j] and so on, up until the end of the array. When we’ve finished, if any a[i] ≥ log(x), then x + i is y-smooth.