More on \(\phi\) in 2016

Find the minimum value of \(k\) that makes \(y\) an integer.

\[\large{y= \log_{\phi(30^3)}\left(30^k \prod_{d \mid 30^3}\phi(d)\right)}\]

Notation: \(\phi(x)\) denotes the Euler totient function.


Inspiration.

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