Uncertainty in a theorem about Sarrus numbers

Question

From https://oeis.org/A001567 there is a theorem of Ray Chandler formulated:

An odd composite number $2n + 1$ is in the sequence if and only if multiplicative order of $2\;(\text{mod}(2n+1))$ divides $2n$.

I suppose that "in the sequence" refers to the sequence of pseudoprimes, composites $n$ such that $n|2^{n-1}-1$, but I don't understand the formulation of this theorem. Is it a typo in the text?

Answer 1

It seems like you miscopied the text in your question. It actually says that:

An odd composite number $2n + 1$ is in the sequence if and only if multiplicative order of $2 \pmod{(2n+1)}$ divides $2n$.

So Chandler's theorem states that, if $2^k \equiv 1 \pmod{(2n+1)}$, then $k | 2n$.