Numbers with similar powers Given an integer p &gt; 1, find the smallest integer q &gt; p such that the list of exponents in the prime factorization of q is the same of that of p, no matter the order or the value of the prime factors.
Examples
The prime factorization of p = 20 is 22 x 51. The smallest integer greater than p with identical exponents in its prime factorization is q = 28 = 22 x 71.
The prime factorization of p = 2500 is 22 x 54. The smallest integer greater than p with identical exponents in its prime factorization is q = 2704 = 24 x 132.
Rules

The input is guaranteed to be an integer greater than 1.
This is code-golf, so the shortest answer in bytes wins.

Test cases
Input | Output
------+-------
2     | 3
20    | 28
103   | 107
256   | 6561
768   | 1280
2500  | 2704
4494  | 4510
46552 | 46584
75600 | 105840
Husk, 10 bytes
§ḟ¤≡ȯÖLgp→

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Explantion
§ḟ       →     Find the first number starting from the input + 1 such that...
        p        The prime factorisation
       g         with equal elements grouped together
    ȯÖL          and sorted by length of groups
  ¤≡             has the same shape as the above applied to the input.