579085261 is CRAZY, 725582 is GOLF, 10757494 is ...?

Jelly, 29 27 bytes

ÆEµØA“¡3ḅḲ+Ṿɼ¡ẏƙẊƘ’œ?xḊṚḢ}¡

Thanks to @JonathanAllan for golfing off 1 byte!

Try it online!

Background

“¡3ḅḲ+Ṿɼ¡ẏƙẊƘ’

is a numeric literal. The characters between the quotes are replaced with their 1-based indices in the Jelly code page, and the resulting array is interpreted as a base-250 number. This yields the integer c := 288824892868083015619552399.

How it works

ÆEµØA“¡3ḅḲ+Ṿɼ¡ẏƙẊƘ’œ?xḊṚḢ}¡  Main link. Argument: n

ÆE                           Yield the exponents of n's prime factorization, with.
                             zeroes. This yields an array A.
  µ                          Begin a new monadic chain with argument A.
   ØA                        Set the return value to “ABC...XYZ”.
     “¡3ḅḲ+Ṿɼ¡ẏƙẊƘ’œ?        Select the c-th permutation of the alphabet, yielding
                             s := “SPMFLQUIXNCWORAGZTEJHVDBKY”.
                      Ḋ      Dequeue; yield A without its first element, stripping
                             the exponent of 2.
                     x       Repeat the k-th letter of s r times, where r is the
                             exponent of the k-th odd prime number.
                          ¡  Combine the two links to the left into a quicklink:
                        Ḣ}     - Apply head to the right argument (A), yielding the
                                 exponent of 2. Since n is at most divisible by the
                                 first power of 2, this yields 1 for even numbers
                                 and 0 for odd ones. Call the link to the left that
                                 many times on the previous return value.
                       Ṛ       - Reverse the string to the left.

Jelly, 36 bytes

“¡3ḅḲ+Ṿɼ¡ẏƙẊƘ’œ?ØA1;;⁶
×107ÆE¢×UḢ¡t⁶

Try it online!

Explanation

Helper constant 1£ (produces “SPMFLQUIXNCWORAGZTEJHVDBKY ” with a 1 prepended)

“¡3ḅḲ+Ṿɼ¡ẏƙẊƘ’œ?ØA1;;⁶
“¡3ḅḲ+Ṿɼ¡ẏƙẊƘ’          288824892868083015619552399 (compressed representation)
              œ?ØA      th permutation of the alphabet
                  1;    prepend 1
                    ;⁶  append a space

Main program

×107ÆE¢×UḢ¡t⁶
×107           Multiply {the input} by 107
    ÆE         Convert to a list of frequencies for each factor
      ¢×       {Vectorized} multiply by the return value of 1£
        UḢ¡    Delete the first value, reverse the list that many times
           t⁶  Delete trailing/leading space

I have a feeling that my compression of the list easily beats the other Jelly answer, but that my algorithm for using it could be a lot more efficient. Maybe I'll try to combine them.

Jelly, 31 bytes, inspired by @Leakynun's answer

“¡3ḅḲ+Ṿɼ¡ẏƙẊƘ’œ?ØA⁷;
ÆfÆCị¢U⁸¡U

Try it online! (slightly modified to run a lot faster)

Is inconsistent in whether it prints a trailing newline (but PPCG normally allows answers either with or without a trailing newline, so I guess this works too?). Is very slow (O(n) where n is the input, and those numbers aren't exactly small…)

Explanation

Helper constant 1£ (produces “¶SPMFLQUIXNCWORAGZTEJHVDBKY”, where ¶ is newline)

“¡3ḅḲ+Ṿɼ¡ẏƙẊƘ’œ?ØA⁷;
“¡3ḅḲ+Ṿɼ¡ẏƙẊƘ’          288824892868083015619552399 (compressed representation)
              œ?ØA      th permutation of the alphabet
                  ⁷;    prepend newline

Main program

ÆfÆCị¢U⁸¡U
Æf          Produce list of prime factors (repeating repeated factors)
  ÆC        Map the nth prime to n
    ị¢      Index into the output of 1£
      U     Reverse
        ¡   a number of times
       ⁸    equal to the input
         U  Reverse again

05AB1E, 39 38 bytes

ÒW<iR¨}26LØR•6Ê2"£´õþÕàçŸôëÂÛ*™•36BS:J

Uses the CP-1252 encoding. Try it online!