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What is the largest number that can divide two numbers without a remainder? What is the smallest number that is divisible by two numbers without a remainder? See more

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

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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\[\large \sum_{n=1}^\infty \dfrac{\gcd(n,2016)}{n^2}= \dfrac{a}{b}\pi^2\]

If the equation above holds true for positive integers \(a\) and \(b\), find \(a+b\).

**Clarification**:

\(\gcd(m,n) \) denotes the greatest common divisor of \(m\) and \(n\).

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