prog.sf

#!/usr/bin/ruby

# a(n) is the smallest integer that has exactly n Lucas divisors (A000032).
# https://oeis.org/A356062

# Known terms:
#   1, 2, 4, 12, 36, 252, 2772, 52668, 1211364, 35129556, 1089016236, 44649665676, 2098534286772, 417608323067628, 88115356167269508, 24760415083002731748, 7948093241643876891108, 4140956578896459860267268

func a(n) {

    return 2 if (n == 2)

    var max = lcm(^n -> map{.lucas})
    var arr = (0..Inf -> lazy.map{.lucas}.while { _ <= max }.grep{.divisors.count{.is_lucas} <= n})

    var tt = Set(arr...)

    for k in (arr) {
        tt = tt.map { (_, lcm(_, k)) }.grep{ _ <= max }
    }

    tt.sort.first{.divisors.count{.is_lucas} == n}
}

for n in (1..20) {
    say "a(#{n}) = #{a(n)}"
}

__END__
a(1) = 1
a(2) = 2
a(3) = 4
a(4) = 12
a(5) = 36
a(6) = 252
a(7) = 2772
a(8) = 52668
a(9) = 1211364
a(10) = 35129556
a(11) = 1089016236
a(12) = 44649665676
a(13) = 2098534286772