Pairs of Consecutive Integers with 6 Divisors

Theorem
The following sequence of integers are those $n$ which fulfil the equation:
 * $\map {\sigma_0} n = \map {\sigma_0} {n + 1} = 6$

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

That is, they are the first of pairs of consecutive integers which each have $6$ divisors:
 * $44, 75, 98, 116, 147, 171, 242, 243, 244, 332, \ldots$

Proof
From Divisor Counting Function from Prime Decomposition:
 * $\ds \map {\sigma_0} n = \prod_{j \mathop = 1}^r \paren {k_j + 1}$

where:
 * $r$ denotes the number of distinct prime factors in the prime decomposition of $n$
 * $k_j$ denotes the multiplicity of the $j$th prime in the prime decomposition of $n$.