MathDB

Let

A

be the set of positive integers that have no prime factors other than

2

3

, or

5

. The infinite sum

\frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{8} + \frac{1}{9} + \frac{1}{10} + \frac{1}{12} + \frac{1}{15} + \frac{1}{16} + \frac{1}{18} + \frac{1}{20} + \cdots

of the reciprocals of the elements of

A

can be expressed as

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. What is

m+n

<span class='latex-bold'>(A)</span> \text{ 16} \qquad <span class='latex-bold'>(B)</span> \text{ 17} \qquad <span class='latex-bold'>(C)</span> \text{ 19} \qquad <span class='latex-bold'>(D)</span> \text{ 23} \qquad <span class='latex-bold'>(E)</span> \text{ 36}

Problem Statement