2015 Fermat Problem 25

There are F fractions \frac{m}{n} with the properties:

- m and n are positive integers with m < n, - \frac{m}{n} is in lowest terms, - n is not divisible by the square of any integer larger than 1, and - the shortest sequence of consecutive digits that repeats consecutively and indefinitely in the decimal equivalent of \frac{m}{n} has length 6.

(Note: The length of the shortest sequence of consecutive digits that repeats consecutively and indefinitely in 0.12\overline{745} = 0.12745745745745\ldots is 3 and the length of the shortest sequence of consecutive digits that repeats consecutively and indefinitely in 0.\overline{5} is 1.)

We define G = F + p, where the integer F has p digits. What is the sum of the squares of the digits of G?

\textbf{(A)}\ 170\quad \textbf{(B)}\ 168\quad \textbf{(C)}\ 217\quad \textbf{(D)}\ 195\quad \textbf{(E)}\ 181

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.