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 A384396 #5 Jun 05 2025 09:54:25
%S A384396 1,5,11,13,17,19,62,23,111,29,123,31,129,217,37,141,106,41,159,391,
%T A384396 118,43
%N A384396 Position of first appearance of n in A384389 (proper choices of disjoint strict partitions of each prime index).
%C A384396 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.
%C A384396 By "proper" we exclude the case of all singletons, which is disjoint when n is squarefree.
%t A384396 prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A384396 pofprop[y_]:=Select[DeleteCases[Join@@@Tuples[IntegerPartitions/@y],y],UnsameQ@@#&];
%t A384396 lv=Table[Length[pofprop[prix[n]]],{n,100}];
%t A384396 mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
%t A384396 Table[Position[lv,x][[1,1]],{x,0,mnrm[lv+1]-1}]
%Y A384396 Positions of first appearances in A384389.
%Y A384396 A000041 counts integer partitions, strict A000009.
%Y A384396 A048767 is the Look-and-Say transform, fixed points A048768, counted by A217605.
%Y A384396 A055396 gives least prime index, greatest A061395.
%Y A384396 A056239 adds up prime indices, row sums of A112798.
%Y A384396 A239455 counts Look-and-Say partitions, ranks A351294
%Y A384396 A351293 counts non-Look-and-Say partitions, ranks A351295.
%Y A384396 Cf. A382912, A383710, A382913, A383708.
%Y A384396 Cf. A179009, A279790, A357982, A381454, A382525, A383706, A384321, A384322, A384347, A384349, A384390, A384393.
%K A384396 nonn,more
%O A384396 0,2
%A A384396 _Gus Wiseman_, Jun 03 2025