Melissa has noticed that certain positive integers can be written as the product of other integers, none of which uses any of the digits in the number itself, 512, for example (512 = 4 x 4 x 8).
Ten consecutive positive integers cannot all be one of Melissa's numbers (A371862 in the OEIS). What about nine? And if not, what is the longest sequence of consecutive numbers all of which are Melissa's numbers?