How to find a number $n$ such that $$\frac{n}{\phi(n)} > 10,$$ where $\phi(n)$ denotes the Euler's phi function?
I was trying to find the smallest one, so was keeping each prime once. I tried with the number $$n = 2\times3\times5\times7\times11\times13\times17\times19$$ and some more numbers, but not working. Need some help!
Note that $$\phi(n) = n \times \prod_{p} \left(1-\frac1p \right) = n \times \prod_{p} \left(\frac{p-1}{p} \right)$$ hence $$\frac{n}{\phi(n)} = \prod_{p} \left(\frac{p}{p-1} \right).$$