[Solution] Sum of Reciprocals of smooth numbers

 Problem is here: https://ruffnsluff.blogspot.com/2021/09/sum-of-reciprocals-of-smooth-numbers.html

$a_n$ = $3^i 5^j$ for some $i ,j \ge 0$

Thus we have that

$$\sum_{k=1}^{n} \frac{1}{a_k} < \sum_{r=0}^{\infty}\frac{1}{3^r} \sum_{s=0}^{\infty} \frac{1}{5^s} = \frac{1}{1- \frac{1}{3}} \frac{1}{1 - \frac{1}{5}} = \frac{15}{8}$$