A number theory problem by Pi Han Goh

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

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.

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