Composite numbers k with no single digit factors whose factors are all substrings of k

Find the composite numbers k in base 10, that have no single digit prime factors and whose prime factors are all a substring of k.

Task

Find and show here, on this page, the first ten elements of the sequence.

Stretch

Find and show the next ten elements.

Julia

<lang julia>using Lazy using Primes

containsitsonlytwodigfactors(n) = (s = string(n); !isprime(n) && all(t -> length(t) > 1 && contains(s, t), map(x -> string(x), collect(keys(factor(n))))))

seq = @>> Lazy.range(2) filter(containsitsonlytwodigfactors)

foreach(p -> print(lpad(last(p), 9), first(p) == 10 ? "\n" : ""), enumerate(take(20, seq)))

</lang>

Output:

    15317    59177    83731   119911   183347   192413  1819231  2111317  2237411  3129361
  5526173 11610313 13436683 13731373 13737841 13831103 15813251 17692313 19173071 28118827

Raku

<lang perl6>use Prime::Factor; use Lingua::EN::Numbers;

put (2..∞).hyper(:5000batch).map( {

   next if (1 < $_ gcd 210) || .is-prime || any .&prime-factors.map: -> $n { !.contains: $n };
   $_

} )[^20].batch(10)».&comma».fmt("%10s").join: "\n";</lang>

Output:

    15,317     59,177     83,731    119,911    183,347    192,413  1,819,231  2,111,317  2,237,411  3,129,361
 5,526,173 11,610,313 13,436,683 13,731,373 13,737,841 13,831,103 15,813,251 17,692,313 19,173,071 28,118,827

Wren

Library: Wren-math

<lang ecmascript>import "/math" for Int import "/fmt" for Fmt

var count = 0 var k = 11 var res = [] while (count < 20) {

   if (k % 3 == 0 || k % 5 == 0 || k % 7 == 0) {
       k = k + 2
       continue
   }
   var factors = Int.primeFactors(k)
   if (factors.count > 1) {
       var s = k.toString
       var includesAll = true
       for (f in factors) {
           if (s.indexOf(f.toString) == -1) {
               includesAll = false
               break
           }
       }
       if (includesAll) {
           res.add(k)
           count = count + 1
       }
   }
   k = k + 2

} Fmt.print("$,10d", res[0..9]) Fmt.print("$,10d", res[10..19])</lang>

Output:

    15,317     59,177     83,731    119,911    183,347    192,413  1,819,231  2,111,317  2,237,411  3,129,361
 5,526,173 11,610,313 13,436,683 13,731,373 13,737,841 13,831,103 15,813,251 17,692,313 19,173,071 28,118,827