cp's OEIS Frontend

A370591 Number of minimal subsets of {1..n} such that it is not possible to choose a different prime factor of each element (non-choosable).

%I A370591 #5 Feb 29 2024 10:48:11
%S A370591 0,1,1,1,2,2,4,4,7,11,16,16,30,30,39,73
%N A370591 Number of minimal subsets of {1..n} such that it is not possible to choose a different prime factor of each element (non-choosable).
%e A370591 The a(1) = 1 through a(10) = 16 subsets:
%e A370591 {1}  {1}  {1}  {1}    {1}    {1}      {1}      {1}      {1}      {1}
%e A370591                {2,4}  {2,4}  {2,4}    {2,4}    {2,4}    {2,4}    {2,4}
%e A370591                              {2,3,6}  {2,3,6}  {2,8}    {2,8}    {2,8}
%e A370591                              {3,4,6}  {3,4,6}  {4,8}    {3,9}    {3,9}
%e A370591                                                {2,3,6}  {4,8}    {4,8}
%e A370591                                                {3,4,6}  {2,3,6}  {2,3,6}
%e A370591                                                {3,6,8}  {2,6,9}  {2,6,9}
%e A370591                                                         {3,4,6}  {3,4,6}
%e A370591                                                         {3,6,8}  {3,6,8}
%e A370591                                                         {4,6,9}  {4,6,9}
%e A370591                                                         {6,8,9}  {6,8,9}
%e A370591                                                                  {2,5,10}
%e A370591                                                                  {4,5,10}
%e A370591                                                                  {5,8,10}
%e A370591                                                                  {3,5,6,10}
%e A370591                                                                  {5,6,9,10}
%t A370591 Table[Length[fasmin[Select[Subsets[Range[n]], Length[Select[Tuples[prix/@#],UnsameQ@@#&]]==0&]]], {n,0,15}]
%Y A370591 Minimal case of A370583, complement A370582.
%Y A370591 For binary indices instead of factors we have A370642, minima of A370637.
%Y A370591 A006530 gives greatest prime factor, least A020639.
%Y A370591 A027746 lists prime factors, indices A112798, length A001222.
%Y A370591 A355741 counts choices of a prime factor of each prime index.
%Y A370591 A367902 counts choosable set-systems, ranks A367906, unlabeled A368095.
%Y A370591 A367903 counts non-choosable set-systems, ranks A367907, unlabeled A368094.
%Y A370591 A368098 counts choosable unlabeled multiset partitions, complement A368097.
%Y A370591 A368100 ranks choosable multisets, complement A355529.
%Y A370591 A368414 counts choosable factorizations, complement A368413.
%Y A370591 A370585 counts maximal choosable sets.
%Y A370591 A370592 counts choosable partitions, complement A370593.
%Y A370591 Cf. A000040, A000720, A045778, A133686, A355739, A355744, A355745, A367771, A370584, A370586, A370587, A370589.
%K A370591 nonn,more
%O A370591 0,5
%A A370591 _Gus Wiseman_, Feb 28 2024