[ROCKY]

1.Let $d(n)$ be the number of perfect squares which are divisors of the number $n$. Show that the average value $\dfrac{d(1)+d(2)+...+d(n)}{n}$ converges as $n$ tends to infinity.
2. Do there exist a quadratic polynomial $P(x)\in\mathbb{R}[x]$ and a positive integer $N$ such that the following inequality
$$\mid p_n-P(n)\mid < 10^{-10000}$$
holds for all integer $n\geq N$, whereas $p_n$ is the nth prime?