experimental-projects/oeis-research/Daniel Suteu/Other/Squarefree 2^d-1 and 2^n-1 not squarefree/7^k - 6^k -- prog.sf

#!/usr/bin/ruby

# Numbers n such that 7^n - 6^n is not squarefree, but 7^d - 6^d is squarefree for every proper divisor d of n.
# https://oeis.org/A280307

# Probably in the sequence:
# 20, 26, 55, 68, 171, 258, 310, 381, 406, 506, 610, 689, 979, 1027, 1081, 1332, 3422, 3775, 3924, 4105, 4422, 4970, 5256, 5430, 5648, 5671, 6123, 6806, 8862, 9218, 9312, 9436, 9591, 9653, 10506

#~ func f(k) {
    #~ k.divisors.first(-1).grep{_ < 150}.all {|d|
        #~ is_prob_squarefree(7**d - 6**d, 1e8)
        #~ #is_squarefree(7**d - 6**d)
    #~ }
#~ }

#~ for k in (1..100) {
    #~ var t = (7**k - 6**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(7**d - 6**d)
        #is_squarefree(7**d - 6**d)
    }
}

for k in (1..30000) {
    var t = (7**k - 6**k)

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