16. The lucky numbers are generated by the following sieving process. Start with the positive integers. Begin the process by crossing out every second integer in the list, starting your count with the integer 1. Other than 1 the smallest integer left is 3 , so we continue by crossing out every third integer left, starting the count with the integer 1 . The next integer left is 7 , so we cross out every seventh integer left. Continue this process, where at each stage we cross out every $k$ th integer left where $k$ is the smallest integer left other than one. The integers that remain are the lucky numbers.
a) Find all lucky numbers less than 100 .
b) Show that there are infinitely many lucky numbers.
16. a) $1,3,7,9,13,15,21,25,31,33,37,43,49,51,63,67,69,73,75,79,87,93,99$