A number theory problem by Pi Han Goh

Number Theory Level 4

$\large a_n = a_{n-1} + \gcd(n,a_{n-1})$

Consider the recurrence relation above with for $n\geq2$ with $a_1 = 7$ . And define $b_n= a_{n+1} - a_n$ , find the number of composite numbers $b_n$ for $n\leq10^9$ .

For the sake of this question, take 1 as neither prime nor composite.