Hayashi's cycle-divisibility conjecture for finite indecomposable quandles

A finite rack $X$ has profile $1^{m_0}l_1^{m_1}l_2^{m_2}\cdots l_k^{m_k}$ when its inner automorphism has $m_0$ cycles of length $1$, $m_1$ cycles of length $l_1$, and so on. Hayashi's conjecture. Let $X$ be a finite indecomposable rack with profile

$$1^{m_0}l_1^{m_1}l_2^{m_2}\cdots l_k^{m_k}.$$

Then $l_i\mid l_k$ for every integer $i$ with $1\leq i\leq k-1$. This conjecture concerns restrictions on the cycle lengths of inner automorphisms of finite indecomposable racks and extends Hayashi's proposed statement for finite connected quandles. The source verifies some cases but does not establish the conjecture in general.