2022 SSMO Relay Round 5 Problems/Problem 2

Problem

Let $T=$ TNYWR, and let $S=\{a_1,a_2,\dots,a_{2022}\}$ be a sequence of 2022 positive integers such that $a_1\le a_2\le \cdots \le a_{2022}$ and $\text{lcm}(a_1,a_2,\dots,a_{2022})=70T$ . Also, $\text{gcd}(a_i,a_j)=1$ for all $1\le i<j\le2022$ . Find the number of possible sequences $S$ .

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2022 SSMO Relay Round 5 Problems/Problem 2

Problem

Solution