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Infinitely many N-tuples of n-free numbers

Source: KoMaL A. 863

December 12, 2023
number theoryAnalytic Number Theorykomal

Problem Statement

Let n≥2n\ge 2 be a given integer. Find the greatest value of NN, for which the following is true: there are infinitely many ways to find NN consecutive integers such that none of them has a divisor greater than 11 that is a perfect nthn^{\mathrm{th}} power.
Proposed by Péter Pál Pach, Budapest
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