Swap prime exponents with their neighbours (Follow-up to my question about swapping bits with their neighbours.)
Task
Given a positive integer x = (2a · 3b) · (5c · 7d) · (11e · 13f) · …, print the integer obtained by swapping the exponents in this factorization for each successive pair of primes, y = (2b · 3a) · (5d · 7c) · (11f · 13e) · …
A061898 in the OEIS. This is code-golf, so the shortest program (in bytes) wins!
Test cases
1 -&gt; 1
2 -&gt; 3
3 -&gt; 2
10 -&gt; 21
37 -&gt; 31
360 -&gt; 756
12345 -&gt; 11578
67895678 -&gt; 125630871
Jelly, 10 bytes

ÆE;0s2UFÆẸ


Try it online! or verify all test cases.

How it works

ÆE;0s2UFÆẸ  Main link. Argument: n

ÆE          Yield the exponents of n's prime factorization.
  ;0        Append a zero.
    s2      Split into pairs.
      U     Upend; reverse each pair.
       F    Flatten the resulting list of pairs.
        ÆẸ  Convert the prime exponents to integer.