We define a positive integer to be multiplicative if it can be written as the sum of three distinct positive integers $x, y, z$ such that $y$ is a multiple of $x$ and $z$ is a multiple of $y$ . Find the sum of all the positive integers which are not multiplicative.

Solution 1

The positive integers which are not multiplicative are $1, 2, 3, 4, 5, 6, 8, 12, 24$ . These sum to $\boxed{65}$ .

2019 CIME I (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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2019 CIME I Problems/Problem 11

Solution 1

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