MathNet 2025 — Part 01 (100 complete bilingual questions) Question 62

Find all integers $n \ge 2$ so that $n$ is divisible by each of the numbers $d_1, d_1+d_2, \dots, d_1+d_2+\dots+d_{k-1}$, where $1 = d_1 \lt d_2 \lt \dots \lt d_{k-1} \lt d_k = n$ are all the positive divisors of $n$.