  Given a positive integer $n$, the factorial base representation of $n$ is
given by $n=\sum_{i=1}^ka_i\cdot i!$, where $a_k\neq 0$ and $0\leq a_i\leq i$
for all $1\leq i\leq k$. For $e\geq 1$, we define
$S_{e,!}:\mathbb{Z}_{\geq0}\to\mathbb{Z}_{\geq0}$ by $S_{e,!}(0) = 0$ and
$S_{e,!}(n)=\sum_{i=0}^{n}a_i^e$, for $n \neq 0$. For $\ell\geq 0$, we let
$S_{e,!}^\ell(n)$ denote the $\ell$-th iteration of $S_{e,!}$, while
$S_{e,!}^0(n)=n$. If $p\in\mathbb{Z}^+$ satisfies $S_{e,!}(p)=p$, then we say
that $p$ is an $e$-power factoradic fixed point of $S_{e,!}$. Moreover, given
$x\in \mathbb{Z}^+$, if $p$ is an $e$-power factoradic fixed point and if there
exists $\ell\in \mathbb{Z}_{\geq 0}$ such that $S_{e,!}^\ell(x)=p$, then we say
that $x$ is an $e$-power factoradic $p$-happy number. Note an integer $n$ is
said to be an $e$-power factoradic happy number if it is an $e$-power
factoradic $1$-happy number. In this paper, we prove that all positive integers
are $1$-power factoradic happy and, for $2\leq e\leq 4$, we prove the existence
of arbitrarily long sequences of $e$-power factoradic $p$-happy numbers. A
curious result establishes that for any $e\geq 2$ the $e$-power factoradic
fixed points of $S_{e,!}$ that are greater than $1$, always appear in sets of
consecutive pairs. Our last contribution, provides the smallest sequences of
$m$ consecutive $e$-power factoradic happy numbers for $2\leq e\leq 5$, for
some values of $m$.
