How to generalize it?

Find the largest non-negative integer nn such that 2n2^n is a factor 2×3×4××99\left\lfloor\sqrt2\right\rfloor\times\left\lfloor\sqrt3\right\rfloor\times\left\lfloor\sqrt4\right\rfloor\times\cdots\times\left\lfloor\sqrt{99}\right\rfloor


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