  An approximate divisor order is a partial order on the positive integers
$\mathbb{N}^+$ that refines the divisor order and is refined by the additive
total order. A previous paper studied such a partial order on $\mathbb{N}^+$,
produced using the floor function. A positive integer $d$ is a floor quotient
of $n$, denoted $d \,\preccurlyeq_{1}\, n$, if there is a positive integer $k$
such that $d = \lfloor{n / k}\rfloor$. The floor quotient relation defines a
partial order on the positive integers. This paper studies a family of partial
orders, the $a$-floor quotient relations $\,\preccurlyeq_{a}\,$, for $a \in
\mathbb{N}^+$, which interpolate between the floor quotient order and the
divisor order on $\mathbb{N}^+$. The paper studies the internal structure of
these orders.
