MathDB

Let

N

be a positive integer. There are

N

tasks, numbered

1, 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

k

, task

k

begins immediately after all tasks whose numbers are divisors of

k

, not including

k

itself, are completed. [*] Task 1 is the first task to begin, and it begins by itself.
Suppose

N = 2017

. How many minutes does it take for all of the tasks to complete? Which tasks are the last ones to complete?

Problem Statement