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

Composite numbers k with no single digit factors whose factors are all substrings of k is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

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.

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