Ohtsuki's factorial integrality conjecture for homology 3-sphere invariants

Let $M$ be an oriented integral homology 3-sphere, and write Ohtsuki's power series as

$$\tau(M)=1+\sum_{n=1}^{\infty}\lambda_n(M)(t-1)^n.$$

Ohtsuki's factorial integrality conjecture. For every $n\geq 1$ and every integral homology 3-sphere $M$,

$$n!\cdot\lambda_n(M)\in 6\mathbb{Z}.$$

The theorem preceding the conjecture gives $\lambda_2(M)\in 3\mathbb{Z}$, while $\lambda_1(M)\in 6\mathbb{Z}$; these divisibility results motivate the conjecture, whose resolution is not specified in the source.