Is there a repdigit that is powerful number(Achilles numbers)?
Powerful numbers(Achilles Numbers) are the numbers whose exponents in prime factors is greater than $1$, but not possible to write it as a perfect power.(Ex. $3528$)
We know that repdigit is never a perfect power as said in this post, but how about being a powerful number?
There are some cases which $\underbrace{n\cdots nn}_{x\text{ times}}$ cannot be a powerful number, such when $n=2, 5, 6$.
In some cases, it is dependent, for example, if $n=3$, then it can be only powerful if $x\equiv1\pmod{3}$, or if $n=7$, then $x\equiv0\pmod{6}$ in order to be powerful number.
I used Paridroid to check if are there any repdigit that is powerful number, but I didn’t find one.