3^k - 2^k -- prog.sf

#!/usr/bin/ruby

# Numbers n such that 3^n - 2^n is not squarefree, but 3^d - 2^d is squarefree for all proper divisors d of n.
# https://oeis.org/A280203

func f(k) {
    k.divisors.first(-1).grep{_ < 150}.all {|d|
        #is_prob_squarefree(2**d - 1, 1e8)
        is_squarefree(3**d - 2**d)
    }
}

#~ From ~~~~: (Start)
#~ The following numbers are also in the sequence: {689, 732, 776, 903, 1055, 1081, 1332, 2525, 2628, 13861}.
#~ Probably, the following numbers are also terms: {2054, 3422, 6416, 6482, 6516, 6806, 9591, 9653, 10386, 10506, 11026, 11342, 11772, 12656, 13203, 14878, 15657, 15922}. (End)

# Smooth 10^4
# 10, 11, 42, 52, 57, 203, 272, 497, 689, 732, 776, 903, 1055, 1081, 1332, 2054, 2525, 2628, 3422, 6416, 6482, 6516, 6806, 9591, 9653, 10386, 10506, 11026, 11342, 11772, 12656, 13203, 13861, 14878, 15657, 15922

# Smooth 10^7
# 10, 11, 42, 52, 57, 203, 272, 497, 689, 732, 776, 903, 1055, 1081, 1332, 2054, 2525, 2628, 3422, 6416, 6482, 6516, 6806

for k in (
 6806, 9591, 9653, 10386, 10506, 11026, 11342, 11772, 12656, 13203, 13861, 14878, 15657, 15922,
) {
    var t = (3**k - 2**k)

    if (!t.is_prob_squarefree(1e7) && f(k)) {
        say k
    }
    else {
        say "Counter-example: #{k}"
    }
}

__END__

func f(k) {
    k.divisors.first(-1).all {|d|
        is_prob_squarefree(3**d - 2**d)
    }
}

for k in (1..30000


) {
    var t = (3**k - 2**k)

    if (!t.is_prob_squarefree(1e6) && !t.is_prob_squarefree && f(k)) {
        print(k, ", ")
    }
}

6, 20, 21, 110, 136, 155, 253, 364, 602, 657, 812, 889, 979, 1081,