Tau Numbers

Tau  numbers are those that  number of divisors of n divides n 
You can see the definition here A033950 and the list of the first 10,000 of these numbers here.
The current year, 2016, is one of these numbers because the number of divisors of 2016 is 36, and 2016/36 = 56.

If we subtract from 2016 his number of divisors 36, we obtain 1980, which is also a number Tau. 
We follow with the same procedure with the numbers obtained while Tau numbers are obtain.

2016 (36) -> 1980 (36) ---> 1944 (24) ---> 1920 (32) and here the chain ends because 1888 is not a number Tau.
 
We can say that 2016 generates (counting himself) four numbers Tau.


What is the longest string of numbers Tau that applying this methodology can be found?

Spanish Version : 1453 - Números Tau