MathDB

6

Part of 2017 Canadian Mathematical Olympiad Qualification

Problems(1)

Division of labor

Source: Canada Repêchage 2017/6

4/13/2017
Let NN be a positive integer. There are NN tasks, numbered 1,2,3,…,N1, 2, 3, \ldots, N, to be completed. Each task takes one minute to complete and the tasks must be completed subjected to the following conditions:
[*] Any number of tasks can be performed at the same time. [*] For any positive integer kk, task kk begins immediately after all tasks whose numbers are divisors of kk, not including kk itself, are completed. [*] Task 1 is the first task to begin, and it begins by itself.
Suppose N=2017N = 2017. How many minutes does it take for all of the tasks to complete? Which tasks are the last ones to complete?
number theory