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Minimum Totient Quotient

Let ϕ(n)\phi(n) be the Euler phi function. If 1n10001 \leq n \leq 1000, what is the smallest integer value of nn that minimizes ϕ(n)n?\frac{\phi(n)}{n}?

You may choose to read Euler's theorem.

Details and Assumptions:

  • You are asked to find the value of nn, not ϕ(n)n \frac {\phi(n) } {n} .
  • ϕ(1)=1\phi(1) = 1 by definition.

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