Question 95
Consider the sequence of integers $a_0, a_1, a_2, \dots$, where $a_n = n^6 - 2017$ if $n$ is divisible by $7$, and $a_n = \frac{1}{7}(n^6 - 2017)$ otherwise. Determine the largest length a string of consecutive terms sharing a common divisor greater than $1$ may have.