This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A330998 #8 Jan 08 2020 09:45:57
%S A330998 1,3,5,6,7,9,10,12,14,15,16,18,19,20,21,22,23,24,25,27,28,29,30,31,33,
%T A330998 34,35,36,37,38,40,41,42,43,44,45,46,47,49,51,52,53,54,56,57,58,59,60,
%U A330998 61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79
%N A330998 Sorted list containing the least number whose inverse prime shadow (A181821) has each possible nonzero number of factorizations into factors > 1.
%C A330998 This is the sorted list of positions of first appearances in A318284 of each element of the range A045782.
%C A330998 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. The inverse prime shadow of n is the least number whose prime exponents are the prime indices of n.
%e A330998 Factorizations of the inverse prime shadows of the initial terms:
%e A330998 4 8 12 16 36 24 60 48
%e A330998 2*2 2*4 2*6 2*8 4*9 3*8 2*30 6*8
%e A330998 2*2*2 3*4 4*4 6*6 4*6 3*20 2*24
%e A330998 2*2*3 2*2*4 2*18 2*12 4*15 3*16
%e A330998 2*2*2*2 3*12 2*2*6 5*12 4*12
%e A330998 2*2*9 2*3*4 6*10 2*3*8
%e A330998 2*3*6 2*2*2*3 2*5*6 2*4*6
%e A330998 3*3*4 3*4*5 3*4*4
%e A330998 2*2*3*3 2*2*15 2*2*12
%e A330998 2*3*10 2*2*2*6
%e A330998 2*2*3*5 2*2*3*4
%e A330998 2*2*2*2*3
%e A330998 The corresponding multiset partitions:
%e A330998 {11} {111} {112} {1111} {1122} {1112}
%e A330998 {1}{1} {1}{11} {1}{12} {1}{111} {1}{122} {1}{112}
%e A330998 {1}{1}{1} {2}{11} {11}{11} {11}{22} {11}{12}
%e A330998 {1}{1}{2} {1}{1}{11} {12}{12} {2}{111}
%e A330998 {1}{1}{1}{1} {2}{112} {1}{1}{12}
%e A330998 {1}{1}{22} {1}{2}{11}
%e A330998 {1}{2}{12} {1}{1}{1}{2}
%e A330998 {2}{2}{11}
%e A330998 {1}{1}{2}{2}
%t A330998 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A330998 nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]],{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t A330998 nds=Table[Length[facs[Times@@Prime/@nrmptn[n]]],{n,50}];
%t A330998 Table[Position[nds,i][[1,1]],{i,First/@Gather[nds]}]
%Y A330998 Taking n instead of the inverse prime shadow of n gives A330972.
%Y A330998 Factorizations are A001055, with image A045782, with complement A330976.
%Y A330998 Factorizations of inverse prime shadows are A318284.
%Y A330998 Cf. A025487, A033833, A045778, A045783, A181819, A181821, A318286, A325238, A330973, A330989, A330990, A330993, A330997.
%K A330998 nonn
%O A330998 1,2
%A A330998 _Gus Wiseman_, Jan 07 2020