Pomerance's conjecture on the count of central binomial coefficients coprime to 105

Let $G(N)$ be the number of positive integers $n eleq N$ such that the central binomial coefficient $\binom{2n}{n}$ is coprime to $105$. Pomerance's conjecture. For all sufficiently large integers $N$,

$$N^{0.025}\leq G(N)\leq N^{0.026}.$$

This conjecture arose from Pomerance's heuristic analysis of Graham's problem and remains open.