Let d(n) denote the number of divisors of n (including itself). You are given that
$$\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}.$$
Find p(6), where p(x) is the unique polynomial with rational coefficients satisfying
$$p(\pi) = \sum_{n=1}^{\infty} \frac{d(n)}{n^2}.$$