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MATH / If n is an integer, such that 2≤n≤2010, for how many values of n is left(1 + frac 12 right)left(1 + frac 13 right) dotsm left(1 + frac 1n right) equal to a positive integer?

Problem

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problem

If nn is an integer, such that 2≤n≤20102 \le n \le 2010, for how many values of nn is $\left(1 + \frac 12 \right)\left(1 + \frac 13 \right) \dotsm \left(1 + \frac 1n \right)$ equal to a positive integer?
Plain-text mathematical notation (without MathML)
If n is an integer, such that 2≤n≤2010, for how many values of n is $\left(1 + \frac 12 \right)\left(1 + \frac 13 \right) \dotsm \left(1 + \frac 1n \right)$ equal to a positive integer?
Original LaTeX notation
If $n$ is an integer, such that $2 \le n \le 2010$, for how many values of $n$ is $\left(1 + \frac 12 \right)\left(1 + \frac 13 \right) \dotsm \left(1 + \frac 1n \right)$ equal to a positive integer?

level

Level 3

type

Intermediate Algebra

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Source and history

task_id
246d8f18-9c02-5836-a7dd-9a2f37224fc4
task_key
intermediate~5falgebra--test--246d8f18-9c02-5836-a7dd-9a2f37224fc4
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import