jmc

Let's find the prime factorization of 436,995: $436,995=3^4\cdot 5395=3^4\cdot 5\cdot 1079=3^4\cdot 5\cdot 13\cdot 83$. We see that $3^2\cdot 83=747$ is a three-digit palindrome, and the product of the remaining powers of primes is a palindrome as well: $3^2\cdot 5\cdot 13=585$. Thus, the desired sum is $747+585=\boxed{1332}$.