Not sure

The number $\boxed{789634}$ has the prime factorization $2\times394817$ is a product of $2$ and a prime number that is congruent to $1$ modulo $4$ . Both of these primes are reducible in the Gaussian integers $\mathbb{Z}[i]$ , and hence $789634$ can be written as a sum of two squares. In fact it is equal to $795^2 + 397^2$ .

The other numbers have prime factorisations (in order) $2^3 \times 19507$ , $2^9 \times 3 \times 97$ , $23 \times 8599$ , $2^6 \times 3^7$ , $47 \times 3617$ . In each case there is a prime factor with odd index that is congruent to $3$ modulo $4$ . In order, these could be $19507, 97, 23, 3, 47$ . Since such primes are irreducible in the Gaussian integers, these numbers cannot be written as a sum of squares.