# 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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