Consecutive Square-Infected Positive Integers

There are \(k\) consecutive positive integers, none of which is square-free.

What is the sum of all possible values of \(k\leq2017\)?

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Details and Assumptions:

  • A positive integer \(n\) is square-free if there is no positive integer \(k>1\) such that \(k^2 \Big|\, n\).

  • Before solving this, you may want to solve this and this .

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