I need help with sequences

Cai writes down the list of positive integers, excluding squares and cubes and all perfect powers. His sequence starts 2, 3, 5, 6, 7, 10, 11, ... What is the 100th term in Cai's list?

Which numbers are missing from your list:

2, 3, 5, 6, 7, 10, 11, ...

All the missing numbers are squares, cubes and perfect powers. Do you think you can continue the list?