15. (12 points) An array composed of certain non-zero natural numbers has the following properties:
(1) Each number in this array (except 1) is divisible by at least one of the numbers 2, 3, or 5.
(2) For any non-zero natural number \( n \), if this array contains one of \( 2n \), \( 3n \), or \( 5n \), then this array must also contain \( n \), \( 2n \), \( 3n \), and \( 5n \).
If the number of elements in this array is between 300 and 400, then this array contains \(\qquad\) elements.
15. (12 points) An array composed of certain non-zero natural numbers has the following properties:
(1) Each number in this array (except 1) can be divided by at least one of the numbers 2, 3, or 5.
(2) For any non-zero natural number \( n \), if this array contains one of \( 2n, 3n, 5n \), then this array must also contain \( n, 2n, 3n, \) and \( 5n \).
If the number of elements in this array is between 300 and 400, then this array contains 364 numbers.
【Solution】: From the problem, let's assume \( N = 2^x \times 3^y \times 5^z \) (where \( x, y, z \) are natural numbers, \( x + y + z \leq n \), and the highest power is \( n \)).
(1) When \( x + y + z = 0 \), \( x = y = z = 0 \), \( N = 1 \), which is valid. In this case, there is 1 number;
(3) When \( x + y + z = 2 \), \( x = y = 1, z = 0 \) or \( x = z = 1, y = 0 \) or \( x = 0, y = z = 1 \) or \( x = 2, y = z = 0 \) or \( x = z = 0, y = 2 \) or \( x = y = 0, z = 2 \),
so \( N = 6 \) or 10 or 15 or 4 or 9 or 25, which is valid. In this case, there are 6 numbers;
(4) When \( x + y + z = n \), there are \( C_{n+2}^{2} \) valid numbers, so in total, \( N = C_{2}^{2} + C_{3}^{2} + \cdots + C_{n+2}^{2} \) valid numbers.
From the problem, the number of elements in this array is between 300 and 400, so \( N = C_{2}^{2} + C_{3}^{2} + \cdots + C_{n+2}^{2} = 1 + 2 + \cdots + 78 = 364 \) valid numbers.
Therefore, the answer is 364.