Question 24
Let $n$ be a natural number. The finite sequence $\alpha$ of positive integers has, among its terms, exactly $n$ distinct numbers ($\alpha$ can have repeated numbers). Furthermore, if $1$ is subtracted from any of its terms, a sequence is obtained that has, among its terms, at least $n$ distinct positive numbers. What is the minimum value that the sum of all the terms of the sequence $\alpha$ can have?