Minimum Totient Quotient

Number Theory Level 4

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

You may choose to read Euler's theorem.

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Details and Assumptions:

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

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