%I #5 Feb 29 2024 10:48:11
%S 0,1,1,1,2,2,4,4,7,11,16,16,30,30,39,73
%N 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 The a(1) = 1 through a(10) = 16 subsets:
%e {1} {1} {1} {1} {1} {1} {1} {1} {1} {1}
%e {2,4} {2,4} {2,4} {2,4} {2,4} {2,4} {2,4}
%e {2,3,6} {2,3,6} {2,8} {2,8} {2,8}
%e {3,4,6} {3,4,6} {4,8} {3,9} {3,9}
%e {2,3,6} {4,8} {4,8}
%e {3,4,6} {2,3,6} {2,3,6}
%e {3,6,8} {2,6,9} {2,6,9}
%e {3,4,6} {3,4,6}
%e {3,6,8} {3,6,8}
%e {4,6,9} {4,6,9}
%e {6,8,9} {6,8,9}
%e {2,5,10}
%e {4,5,10}
%e {5,8,10}
%e {3,5,6,10}
%e {5,6,9,10}
%t Table[Length[fasmin[Select[Subsets[Range[n]], Length[Select[Tuples[prix/@#],UnsameQ@@#&]]==0&]]], {n,0,15}]
%Y Minimal case of A370583, complement A370582.
%Y For binary indices instead of factors we have A370642, minima of A370637.
%Y A006530 gives greatest prime factor, least A020639.
%Y A027746 lists prime factors, indices A112798, length A001222.
%Y A355741 counts choices of a prime factor of each prime index.
%Y A367902 counts choosable set-systems, ranks A367906, unlabeled A368095.
%Y A367903 counts non-choosable set-systems, ranks A367907, unlabeled A368094.
%Y A368098 counts choosable unlabeled multiset partitions, complement A368097.
%Y A368100 ranks choosable multisets, complement A355529.
%Y A368414 counts choosable factorizations, complement A368413.
%Y A370585 counts maximal choosable sets.
%Y A370592 counts choosable partitions, complement A370593.
%Y Cf. A000040, A000720, A045778, A133686, A355739, A355744, A355745, A367771, A370584, A370586, A370587, A370589.
%K nonn,more
%O 0,5
%A _Gus Wiseman_, Feb 28 2024