2019 CIME I Problems/Problem 11

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 $\boxed{65}$ .
See also

2019 CIME I (Problems • Answer Key • Resources)

Preceded by
Problem 10 Followed by
Problem 12

1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15

All CIME Problems and Solutions
The problems on this page are copyrighted by the MAC's Christmas Mathematics Competitions.

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2019 CIME I Problems/Problem 11

Solution 1

See also

2019 CIME I (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
All CIME Problems and Solutions