For all positive integers $n$ and $m,$ the function $A(n)$ equals the following product:

For all positive integers $n$ and $m,$ the function $A(n)$ equals the following product:
$\left(1 + \dfrac12 + \dfrac1{2^2}\right)\left(1 + \dfrac13 + \dfrac1{3^2}\right)\left(1 +\dfrac15 + \dfrac1{5^2}\right)\cdots\left(1 + \dfrac1{p_n} + \dfrac1{p_n^2}\right),$ where $p_n$ is the $nth$ smallest prime number, while $B(m)$ equals the sum of the reciprocals of all the positive integers from $1$ through $m,$ inclusive. The largest reciprocal of an integer in the sum that $B(25)$ represents that is NOT present in the distributed expansion of $A(5)$ is

A. $\dfrac14$

B. $\dfrac15$

C. $\dfrac16$

D. $\dfrac17$

E. $\dfrac18$

Answer: E

Source: Manhattan GMAT

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