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floor sum of squarefree numbers

Source: Croatia 2000 4th Grade P4

May 9, 2021
number theoryfloor function

Problem Statement

Let SS be the set of all squarefree numbers and nn be a natural number. Prove that ∑k∈S⌊nk⌋=n.\sum_{k\in S}\left\lfloor\sqrt{\frac nk}\right\rfloor=n.
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