sidef-scripts/Math/k-non-powerfree_numbers_in_range.sf

#!/usr/bin/ruby

# Author: Trizen
# Date: 03 May 2023
# https://github.com/trizen

# A simple algorithm for generating the non-(k-powerfree) numbers in a given range [A, B].
# A number is called k-powerfree, if all the exponents in its prime factorization are < k.

func non_powerfree(A, B, k=1) {

    var arr = []

    for j in (2 .. B.iroot(k)) {

        var m = j**k

        for s in (idiv_ceil(A,m) .. idiv(B,m)) {
            if (s.is_powerfree(k)) {
                arr << m*s
            }
        }
    }

    return arr.sort
}

say non_powerfree(65, 100, 2)   #=> [68, 72, 75, 76, 80, 81, 84, 88, 90, 92, 96, 98, 99, 100]
say non_powerfree(64, 150, 3)   #=> [64, 72, 80, 81, 88, 96, 104, 108, 112, 120, 125, 128, 135, 136, 144]