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Least number of factors giving 51/2010

High school · ●●●●○ 100 pts

Find the least positive integer nn for which there exists a set {s1,s2,…,sn}\{s_1, s_2, \ldots, s_n\} consisting of nn distinct positive integers such that (1−1s1)(1−1s2)⋯(1−1sn)=512010.\left(1-\frac{1}{s_1}\right)\left(1-\frac{1}{s_2}\right)\cdots\left(1-\frac{1}{s_n}\right)=\frac{51}{2010}.

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