Question 45
For an integer $a \geq 2$, denote by $\delta(a)$ the second largest divisor of $a$. Let $(a_{n})_{n \geq 1}$ be a sequence of integers such that $a_{1} \geq 2$ and
$$
a_{n+1}=a_{n}+\delta\left(a_{n}\right)
$$
for all $n \geq 1$. Prove that there exists a positive integer $k$ such that $a_{k}$ is divisible by $3^{2022}$.
$$
a_{n+1}=a_{n}+\delta\left(a_{n}\right)
$$
for all $n \geq 1$. Prove that there exists a positive integer $k$ such that $a_{k}$ is divisible by $3^{2022}$.