Some positive integer $n$ is written on the board. Andrey and Petya is playing the following game. Andrey finds all the different representations of the number n as a product of powers of prime numbers (values degrees greater than 1), in which each factor is greater than all previous or equal to the previous one. Petya finds all different representations of the number $n$ as a product of integers greater than $1$, in which each factor is divisible by all the previous factors. The one who finds more performances wins, if everyone finds the same number of representations, the game ends in a draw. Find all positive integers $n$ for which the game will end in a draw.

Note. 
The representation of the number $n$ as a product is also considered a representation consisting of a single factor $n$.
To solve this problem, we need to analyze the two different ways of representing the number \( n \) and show that they yield the same number of representations.

1. **Prime Factorization Representation**:
   - Andrey finds all different representations of \( n \) as a product of powers of prime numbers, where each factor is greater than or equal to the previous one.
   - Let \( n \) have the prime factorization \( n = p_1^{\alpha_1} \cdot p_2^{\alpha_2} \cdots p_m^{\alpha_m} \), where \( p_1, p_2, \ldots, p_m \) are distinct prime numbers and \( \alpha_1, \alpha_2, \ldots, \alpha_m \) are positive integers.

2. **Divisibility Representation**:
   - Petya finds all different representations of \( n \) as a product of integers greater than 1, where each factor is divisible by all the previous factors.
   - This means that if \( n = b_1 \cdot b_2 \cdots b_k \), then \( b_1 \mid b_2 \mid \cdots \mid b_k \).

3. **Counting Representations**:
   - For Andrey's representation, we need to count the number of ways to write \( n \) as a product of powers of primes, where the exponents are non-decreasing.
   - For Petya's representation, we need to count the number of ways to write \( n \) as a product of integers, where each integer is divisible by the previous one.

4. **Nondecreasing Sequences**:
   - The number of nondecreasing sequences of positive integers that sum to \( k \) is denoted by \( f(k) \).
   - For each prime \( p_i \) with exponent \( \alpha_i \), the number of ways to distribute the exponent \( \alpha_i \) into nondecreasing sequences is \( f(\alpha_i) \).

5. **Product of Counts**:
   - The total number of representations for \( n \) in both cases is given by the product of the counts for each prime factor.
   - Therefore, the number of representations for \( n \) is \( \prod_{i=1}^m f(\alpha_i) \).

6. **Conclusion**:
   - Since both Andrey and Petya's representations are counted by the same product \( \prod_{i=1}^m f(\alpha_i) \), they will always find the same number of representations.
   - Hence, the game will always end in a draw for any positive integer \( n \).

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