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A304660 A run-length describing inverse to A181819. The multiplicity of prime(k) in a(n) is the k-th smallest prime index of n, which is A112798(n,k).

%I A304660 #8 Jan 22 2023 18:54:52
%S A304660 1,2,4,6,8,18,16,30,36,54,32,150,64,162,108,210,128,450,256,750,324,
%T A304660 486,512,1470,216,1458,900,3750,1024,2250,2048,2310,972,4374,648,7350,
%U A304660 4096,13122,2916,10290,8192,11250,16384,18750,4500,39366,32768,25410,1296
%N A304660 A run-length describing inverse to A181819. The multiplicity of prime(k) in a(n) is the k-th smallest prime index of n, which is A112798(n,k).
%C A304660 A permutation of A133808. a(n) is the smallest member m of A133808 such that A181819(m) = n.
%F A304660 a(n) = Product_{i = 1..Omega(n)} prime(i)^A112798(n,i).
%e A304660 Sequence of normalized prime multisets together with the normalized prime multisets of their images begins:
%e A304660    1:        {} -> {}
%e A304660    2:       {1} -> {1}
%e A304660    3:       {2} -> {1,1}
%e A304660    4:     {1,1} -> {1,2}
%e A304660    5:       {3} -> {1,1,1}
%e A304660    6:     {1,2} -> {1,2,2}
%e A304660    7:       {4} -> {1,1,1,1}
%e A304660    8:   {1,1,1} -> {1,2,3}
%e A304660    9:     {2,2} -> {1,1,2,2}
%e A304660   10:     {1,3} -> {1,2,2,2}
%e A304660   11:       {5} -> {1,1,1,1,1}
%e A304660   12:   {1,1,2} -> {1,2,3,3}
%e A304660   13:       {6} -> {1,1,1,1,1,1}
%e A304660   14:     {1,4} -> {1,2,2,2,2}
%e A304660   15:     {2,3} -> {1,1,2,2,2}
%e A304660   16: {1,1,1,1} -> {1,2,3,4}
%e A304660   17:       {7} -> {1,1,1,1,1,1,1}
%e A304660   18:   {1,2,2} -> {1,2,2,3,3}
%t A304660 Table[With[{y=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]},Times@@Power[Array[Prime,Length[y]],y]],{n,100}]
%Y A304660 Cf. A055932, A056239, A112798, A130091, A133808, A181819, A181821, A182850, A182857, A275870, A304455.
%K A304660 nonn
%O A304660 1,2
%A A304660 _Gus Wiseman_, May 16 2018