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Counting sets with product a perfect cube

Source: Czech-Polish-Slovak Junior Match 2024, I-2

May 29, 2024
number theorynumber theory proposedProductperfect cubegeometry3D geometry

Problem Statement

How many non-empty subsets of {1,2,…,11}\{1,2,\dots,11\} are there with the property that the product of its elements is the cube of an integer?
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