Definition:Odd Integer/Odd-Times Odd

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Let $n \in \Z$, i.e. let $n$ be an integer.

Definition 1

$n$ is odd-times odd if and only if it is an odd number greater than $1$ which is not prime.

Definition 2

$n$ is odd-times odd if and only if there exist odd numbers $x, y > 1$ such that $n = x y$.


The sequence of odd-times odd integers begins:

$9, 15, 21, 25, 27, \ldots$

Euclid's Definition

In the words of Euclid:

An odd-times odd number is that which is measured by an odd number according to an odd number.

(The Elements: Book $\text{VII}$: Definition $10$)

Also see