Sixfold fun in 2015, Part 38

\[S=\sum_{d|12090}\frac{\phi(d)}{d}\]

Find the smallest positive integer \(a\) such that \(a\times S\) is an integer.

Clarifications

  • The sum \(S\) is taken over all 32 positive integer divisors \(d\) of \(12090=6\times 2015\)

  • \(\phi(d)\) denotes the Euler's totient function.

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