Composite number n such that $\gcd(n-1, \phi(n))$ increases to a record.

Question

With n prime, $\gcd(n-1, \phi(n)) = n-1$, so I don't list with n prime. Composite number n such that $\gcd(k-1, \phi(k)) < \gcd(n-1, \phi(n))$ for every composite number $k < n$. I can't find this list in an OEIS. My list is (from $4$ to $1000000$): $4, 9, 21, 49, 65, 91, 217, 385, 451, 561, 946, 1729, 3201, 6601, 8911, 25761, 30889, 46657, 88561, 158401, 211141, 238465, 334369, 534061, 851201$ and so on, with the value of $\gcd(n-1, \phi(n))$ are: $1, 2, 4, 6, 16, 18, 36, 48, 50, 80, 105, 432, 640, 1320, 1782, 1840, 3432, 5184, 9840, 10560, 12420, 26496, 55728, 59340, 85120$ and so on. So, what's the next number and what do I miss a number of the list from 4 to 1000000?? I want to have the list with 1000 numbers.