Tuesday, September 7, 2021

Sum of reciprocals of smooth numbers

 Let $a_1, a_2, \dots, a_n$ be $n \ge 1$ distinct odd integers with no prime factors $\gt 5$.


Show that


$$ \sum_{i=1}^{n} \dfrac{1}{a_n} \lt \frac{15}{8}$$


[Solution]

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