Question 75
Determine all sequences $(a_n)$ of positive integers such that
$$
\frac{1}{2} \lt \frac{\gcd(a_r, a_s)}{\gcd(r, s)} \lt 2,
$$
for all positive integers $r, s$.
$$
\frac{1}{2} \lt \frac{\gcd(a_r, a_s)}{\gcd(r, s)} \lt 2,
$$
for all positive integers $r, s$.