
COMMENTS

Let m be a product of a primorial, listed by A025487.
Consider the standard form prime power decomposition of m = Product(p^e), where prime p  m (listed from smallest to largest p), and e is the largest multiplicity of p such that p^e  m (which we shall hereinafter simply call "multiplicity").
Products of primorials have a list L of multiplicities in a strictly decreasing arrangement.
A recursively selfconjugate L has a conjugate L* = L. Further, elimination of the Durfee square and leg (conjugate with the arm) to leave the arm L_1. L_1 likewise has conjugate L_1* = L_1. We continue taking the arm, eliminating the new Durfee square and leg in this manner until the entire list L is processed and all arms are selfconjugate.
a(n) is a subsequence of A181825 (m with selfconjugate prime signatures).
Subsequences of a(n) include A006939 and A181555.
This sequence can be produced by a similar algorithm that pertains to recursively selfconjugate integer partitions at A322156.
From Michael De Vlieger, Jan 16 2020: (Start)
2 is the only prime in a(n).
The smallest 2 terms of a(n) are primorials, i.e., in A002110.
The smallest 5 terms of a(n) are highly composite, i.e., in A002182. (End)


EXAMPLE

A025487(1) = 1, the empty product, is in the sequence since it is the product of no primes at all; this null sequence is selfconjugate.
A025487(2) = 2 = 2^1 > {1} is self conjugate.
A025487(6) = 12 = 2^2 * 3 > {2, 1} is self conjugate.
A025487(32) = 360 = 2^3 * 3^2 * 5 > {3, 2, 1} is selfconjugate.
Graphing the multiplicities, we have:
3 x 3 x
2 x x ==> 2 x x
1 x x x 1 x x x
2 3 5 2 3 5
where the vertical axis represents multiplicity and the horizontal the kth prime p, and the arrow represents the transposition of the x's in the graph. We see that the transposition does not change the prime signature (thus, m is also in A181825), and additionally, the prime signature is recursively selfconjugate.


MATHEMATICA

Block[{n = 6, f, g}, f[n_] := Block[{w = {n}, c}, c[x_] := Apply[Times, Most@ x  Reverse@ Accumulate@ Reverse@ Rest@ x]; Reap[Do[Which[And[Length@ w == 2, SameQ @@ w], Sow[w]; Break[], Length@ w == 1, Sow[w]; AppendTo[w, 1], c[w] > 0, Sow[w]; AppendTo[w, 1], True, Sow[w]; w = MapAt[1 + # &, Drop[w, 1], 1]], {i, Infinity}] ][[1, 1]] ]; g[w_] := Block[{k}, k = Total@ w; Total@ Map[Apply[Function[{s, t}, s Array[Boole[t <= # <= s + t  1] &, k] ], #] &, Apply[Join, Prepend[Table[Function[{v, c}, Map[{w[[k]], # + 1} &, Map[Total[v #] &, Tuples[{0, 1}, {Length@ v}]]]] @@ {Most@ #, ConstantArray[1, Length@ #  1]} &@ Take[w, k], {k, 2, Length@ w}], {{w[[1]], 1}}]]] ]; {1}~Join~Take[#, FirstPosition[#, StringJoin["{", ToString[n], "}"]][[1]] ][[All, 1]] &@ Sort[MapIndexed[{Times @@ Flatten@ MapIndexed[Prime[#2]^#1 &, #2], ToString@ #1} & @@ {#1, g[#1], First@ #2} &, Apply[Join, Array[f[#] &, n] ] ] ] ]
(* Second program: decompress dataset of a(n) for n = 0..75047 *)
{1}~Join~Map[Block[{k, w = ToExpression@ StringSplit[#, " "]}, k = Total@ w; Times @@ Flatten@ MapIndexed[Prime[#2]^#1 &, Total@ #] &@ Map[Apply[Function[{s, t}, s Array[Boole[t <= # <= s + t  1] &, k] ], #] &, Apply[Join, Prepend[Table[Function[{v, c}, Map[{w[[k]], # + 1} &, Map[Total[v #] &, Tuples[{0, 1}, {Length@ v}]]]] @@ {Most@ #, ConstantArray[1, Length@ #  1]} &@ Take[w, k], {k, 2, Length@ w}], {{w[[1]], 1}}]]] ] &, Import["https://oeis.org/A330781/a330781.txt", "Data"] ] (* Michael De Vlieger, Jan 16 2020 *)
