Sequence of 4 Consecutive Integers with Equal Number of Divisors

Theorem
The following sequence of integers are sets of $4$ consecutive integers which all have the same number of divisors:
 * $\map {\sigma_0} m = \map {\sigma_0} {m + 1} = \map {\sigma_0} {m + 2} = \map {\sigma_0} {m + 3}$

where $\map {\sigma_0} n$ denotes the divisor count function.


 * $242, 243, 244, 245, 3655, 3656, 3657, 3658, 4503, 4504, 4505, 4506, \ldots$