744*. Find all natural numbers that cannot be represented as the sum of three natural numbers, the product of which is a perfect square.
$\triangle$ First, we will look for all natural numbers that can be represented in such a form. Let's consider two cases.

1) Suppose the natural number $a$ is odd: $a=2k+1$, where $k$ is a natural number.

If $a$ is represented as the sum: $a=k+k+1$, then the product of these three addends is the square of a natural number: $k \cdot k \cdot 1 = k^2$. Therefore, all odd natural numbers starting from 3 can be represented in the required form.

2) Suppose the number $a$ is even: $a=2k$, where $k$ is a natural number.

What should we do in this case?

Probably, by breaking down $a$ into three addends, we need to single out an addend equal to 4, since 4 is a perfect square, and two more equal addends. We get:

$$
a=2k=(2k-4)+4=(k-2)+(k-2)+4
$$

The product of these three addends is the square of a natural number:

$$
(k-2)(k-2)4=((k-2)2)^2
$$

This reasoning is valid only for $k>2$. Therefore, the values $k=1$ and $k=2$ need to be considered separately; then $a=2$ and $a=4$. In addition, in the first case, the number $a=1$ remains.

Checking shows that none of the numbers 1, 2, and 4 can be represented in the required form.

Answer: $1, 2, 4$.