A304660 - OEIS

%I #8 Jan 22 2023 18:54:52

%S 1,2,4,6,8,18,16,30,36,54,32,150,64,162,108,210,128,450,256,750,324,

%T 486,512,1470,216,1458,900,3750,1024,2250,2048,2310,972,4374,648,7350,

%U 4096,13122,2916,10290,8192,11250,16384,18750,4500,39366,32768,25410,1296

%N 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 A permutation of A133808. a(n) is the smallest member m of A133808 such that A181819(m) = n.

%F a(n) = Product_{i = 1..Omega(n)} prime(i)^A112798(n,i).

%e Sequence of normalized prime multisets together with the normalized prime multisets of their images begins:

%e    1:        {} -> {}

%e    2:       {1} -> {1}

%e    3:       {2} -> {1,1}

%e    4:     {1,1} -> {1,2}

%e    5:       {3} -> {1,1,1}

%e    6:     {1,2} -> {1,2,2}

%e    7:       {4} -> {1,1,1,1}

%e    8:   {1,1,1} -> {1,2,3}

%e    9:     {2,2} -> {1,1,2,2}

%e   10:     {1,3} -> {1,2,2,2}

%e   11:       {5} -> {1,1,1,1,1}

%e   12:   {1,1,2} -> {1,2,3,3}

%e   13:       {6} -> {1,1,1,1,1,1}

%e   14:     {1,4} -> {1,2,2,2,2}

%e   15:     {2,3} -> {1,1,2,2,2}

%e   16: {1,1,1,1} -> {1,2,3,4}

%e   17:       {7} -> {1,1,1,1,1,1,1}

%e   18:   {1,2,2} -> {1,2,2,3,3}

%t 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 Cf. A055932, A056239, A112798, A130091, A133808, A181819, A181821, A182850, A182857, A275870, A304455.

%K nonn

%O 1,2

%A _Gus Wiseman_, May 16 2018