The square-free v-palindrome conjecture in base ten

Let $v(n)$ denote the sum of the primes and exponents appearing in the prime factorization of $n$, and let $r_{10}(n)$ be the digit reversal of $n$ in base ten. A $v$-palindrome in base ten is a natural number $n$ with $10 mid n$, $n e r_{10}(n)$, and $v(n)=v(r_{10}(n))$. Square-free $v$-palindrome conjecture. There are infinitely many $v$-palindromes $n$ in base ten such that both $n$ and $r_{10}(n)$ are square-free.

This conjecture asks for an infinite family of $v$-palindromes satisfying the additional square-freeness condition; the source does not specify a resolution.