Question 178
The sequence $a_1, a_2, a_3, \dots$ of positive integers is defined in the following way: $a_1 = 63$ and for each $n \ge 2$ the number $a_n$ is the smallest positive integer divisible by $n$, which is not less than $a_{n-1}$. (For example, $a_2 = 64$, $a_3 = 66, a_4 = 68, a_5 = 70$.)
Prove that each positive integer can occur in this sequence at most once.
Prove that each positive integer can occur in this sequence at most once.