to I to n 2 Doorkeepers to Let n E N. There are n doors and n doorkeepers, which are indexed by integers from 1 to n. All doors are initially closed. Then the doorkeepers, one after another, do the following: Doorkeeper 1 visits all doors and opens them. Doorkeeper 2 visits all doors indexed by even numbers and closed them. Doorkeeper 3 visits all doors indexed by multiples of 3 and opens the closed ones and closes the open ones. In general , Doorkeeper j visits all doors indexed by multiples of j and opens the closed ones and closes the open ones. Your mission, should you choose to accept it, is to write a MATLAB script which, given n, generates a row vector of integers corresponding to the doors that are open at the end. Extra Credit Find a mathematical formula which identifies all open doors at the end. Write clearly your justi- fication. Then write a single MATLAB statement implementing your formula. Confirm that the statement yields the same result as the script you wrote above