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Painting the Integers With Respect To Its Proper Divisors

Source: 2019 AMC 12A #13

February 8, 2019
AMCAMC 12AMC 12 A2019 AMC 12Acounting2019 AMC

Problem Statement

How many ways are there to paint each of the integers 2,3,…,92, 3, \dots, 9 either red, green, or blue so that each number has a different color from each of its proper divisors?
<spanclass=′latex−bold′>(A)</span> 144<spanclass=′latex−bold′>(B)</span> 216<spanclass=′latex−bold′>(C)</span> 256<spanclass=′latex−bold′>(D)</span> 384<spanclass=′latex−bold′>(E)</span> 432<span class='latex-bold'>(A)</span>\ 144\qquad<span class='latex-bold'>(B)</span>\ 216\qquad<span class='latex-bold'>(C)</span>\ 256\qquad<span class='latex-bold'>(D)</span>\ 384\qquad<span class='latex-bold'>(E)</span>\ 432
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