5^k - 4^k -- prog.sf

#!/usr/bin/ruby

# Numbers n such that 5^n - 4^n is not squarefree, but 5^d - 4^d is squarefree for every proper divisor d of n.
# https://oeis.org/A280209

# Probably in the sequence:
# 2, 55, 171, 183, 203, 465, 955, 1027, 1711, 2485, 3197, 4431, 6275, 8515, 10121,

#~ func f(k) {
    #~ k.divisors.first(-1).grep{_ < 150}.all {|d|
        #~ is_prob_squarefree(5**d - 4**d, 1e8)
        #~ #is_squarefree(5**d - 4**d)
    #~ }
#~ }

#~ for k in (1..100) {
    #~ var t = (5**k - 4**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(5**d - 4**d)
        #is_squarefree(5**d - 4**d)
    }
}

for k in (1..30000) {
    var t = (5**k - 4**k)

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