Highly Composite Deficient Numbers

My diurnal age today is 27027 and this factorises as follows:$$27027=3^3 \times 7 \times 11 \times 13$$Although this number, with its many factors and 32 divisors, looks as though it should be abundant, it's not. It just misses the mark because the ratio of the sum of its proper divisors to the number itself just falls short of unity:$$ \begin{align} \frac{ \sigma(27027, 1)-27027}{27027}&=\frac{53760-27027}{27027}\\ &=\frac{26733}{27027} \\ & \approx 0.989121989121989 \end{align}$$On March 24th 2023, I wrote about Balanced Numbers and 27027 is such a number because:$$27027=\overbrace{27}^{2+7=9} \cdot 0 \cdot \overbrace{27}^{2+7=9}$$However, 27027 has a greater claim to fame because it's a member of OEIS A302934:

A302934

Highly composite deficient numbers: deficient numbers \(k\) whose number of divisors \(d(k) \gt d(m) \) for all deficient numbers \(m \lt k\).

The table below shows a list of deficient numbers up to one million that have a record number of divisors. The ratio of the sum of proper divisors to the number is also shown (permalink).

 number   divisors   ratio

  1        1          0.000000000000000
  2        2          0.500000000000000
  4        3          0.750000000000000
  8        4          0.875000000000000
  16       5          0.937500000000000
  32       6          0.968750000000000
  64       7          0.984375000000000
  105      8          0.828571428571429
  225      9          0.791111111111111
  315      12         0.980952380952381
  1155     16         0.994805194805195
  2475     18         0.953939393939394
  4455     20         0.955555555555556
  8775     24         0.978347578347578
  26325    30         0.994833808167142
  27027    32         0.989121989121989
  63063    36         0.974025974025974
  106029   40         0.971988795518207
  247401   48         0.990614427589217
  693693   54         0.988980716253444
  829521   60         0.995464852607710
  969969   64         0.995280261534132

Looking at the table, the status of 27027 as a record breaker can be seen. Deficient numbers can be ranked by their number of divisors or by how close they approach unity (or how close they approach 2 if we prefer to deal with abundancy). I've investigated the latter in a post titled Odd Deficient Numbers from April 30th 2021. Another post on deficient numbers is Gaps Between Deficient Numbers from October 30th 2020. The post Multiperfect, Hyperfect and Superperfect Numbers from July 24th 2019 is also relevant.