Fundamental Neighbors

The fundamental theorem of arithmetic says that any natural
number greater than one can be written uniquely as the product
of prime numbers. For example: $3
= 3^1$, $4 = 2^2$,
$6 = 2^1 \times 3^1$,
$72 = 2^3 \times 3^2$, and
in general,

\[ n =
p_1^{e_1}\times p_2^{e_2}\times \cdots \times p_ k^{e_ k}
\]

for prime numbers $p_1$
through $p_ k$ and
exponents $e_1$ through
$e_ k$.

For this problem, given an integer $n \geq 2$, determine what we will
call the ‘neighbor’ of $n$. The neighbor is the integer you
get by swapping the $p_ i$
and $e_ i$ values in the
prime factorization of $n$. That is, if $n$ is written in prime factorization
as above, the neighbor of $n$ is