Is a composite number
n always either
- a product of two coprimes (i.e. $n = n_1 \cdot n_2$ such that $n_1$ and $n_2$ are coprimes)
- or a power of a prime itself (i.e. $n = x ^ y$ where $x$ is a prime)
I would think this is true since when you factorize $n$, if $n$ have two or more prime factors then those prime factors can be arranged to make $2$ coprimes. Otherwise if $n$ can only be factorized using one prime then it can't be the product of two coprimes.
Is this true? Is there any error in my reasoning?