Pairs of Consecutive Integers with 6 Divisors

Theorem
The following sequence of integers are those $n$ which fulfil the equation:
 * $\tau \left({n}\right) = \tau \left({n + 1}\right) = 6$

where $\tau \left({n}\right)$ denotes the $\tau$ 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 Tau Function from Prime Decomposition:
 * $\displaystyle \tau \left({n}\right) = \prod_{j \mathop = 1}^r \left({k_j + 1}\right)$

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 $n$.