cp's OEIS Frontend

A370587 Number of subsets of {1..n} containing n such that it is not possible to choose a different prime factor of each element (non-choosable).

%I A370587 #9 Mar 28 2025 14:01:19
%S A370587 0,1,1,2,6,10,24,44,116,236,468,908,1960,3776,7812,15876,32504,63744,
%T A370587 130104,257592,521152,1042976,2087096,4166408,8376816,16760832,
%U A370587 33507744,67089280,134169440,268236928,536759984,1073233840,2147384000,4294503744,8589075216,17179048048
%N A370587 Number of subsets of {1..n} containing n such that it is not possible to choose a different prime factor of each element (non-choosable).
%e A370587 The a(0) = 0 through a(5) = 10 subsets:
%e A370587   .  {1}  {1,2}  {1,3}    {1,4}      {1,5}
%e A370587                  {1,2,3}  {2,4}      {1,2,5}
%e A370587                           {1,2,4}    {1,3,5}
%e A370587                           {1,3,4}    {1,4,5}
%e A370587                           {2,3,4}    {2,4,5}
%e A370587                           {1,2,3,4}  {1,2,3,5}
%e A370587                                      {1,2,4,5}
%e A370587                                      {1,3,4,5}
%e A370587                                      {2,3,4,5}
%e A370587                                      {1,2,3,4,5}
%t A370587 Table[Length[Select[Subsets[Range[n]],MemberQ[#,n] && Length[Select[Tuples[If[#==1,{},First/@FactorInteger[#]]&/@#], UnsameQ@@#&]]==0&]],{n,0,10}]
%Y A370587 First differences of A370583, complement A370582, cf. A370584.
%Y A370587 The complement is counted by A370586.
%Y A370587 For a unique choice we have A370588.
%Y A370587 For binary indices instead of factors we have A370639, complement A370589.
%Y A370587 A006530 gives greatest prime factor, least A020639.
%Y A370587 A027746 lists prime factors, indices A112798, length A001222.
%Y A370587 A355741 counts choices of a prime factor of each prime index.
%Y A370587 A367902 counts choosable set-systems, ranks A367906, unlabeled A368095.
%Y A370587 A367903 counts non-choosable set-systems, ranks A367907, unlabeled A368094.
%Y A370587 A368098 counts choosable unlabeled multiset partitions, complement A368097.
%Y A370587 A368100 ranks choosable multisets, complement A355529.
%Y A370587 A368414 counts choosable factorizations, complement A368413.
%Y A370587 A370585 counts maximal choosable sets.
%Y A370587 A370592 counts choosable partitions, complement A370593.
%Y A370587 Cf. A000040, A000720, A005117, A045778, A133686, A355739, A355744, A355745, A367905, A370636.
%K A370587 nonn
%O A370587 0,4
%A A370587 _Gus Wiseman_, Feb 28 2024
%E A370587 More terms from _Jinyuan Wang_, Mar 28 2025