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A370590
Number of maximal subsets of {1..n} containing n such that it is possible to choose a different prime factor of each element (choosable).
3
0, 0, 1, 1, 1, 2, 3, 5, 2, 4, 14, 25, 13, 38, 46, 66, 28, 178, 57
OFFSET
0,6
COMMENTS
For example, the set {4,7,9,10} has choice (2,7,3,5) so is counted under a(10).
EXAMPLE
The a(0) = 0 through a(10) = 14 subsets (A = 10):
. . 2 23 34 235 256 2357 3578 2579 237A
345 356 2567 5678 4579 267A
456 3457 5679 279A
3567 5789 347A
4567 357A
367A
378A
467A
479A
567A
579A
678A
679A
789A
MATHEMATICA
Table[Length[Select[Subsets[Range[n], {PrimePi[n]}], MemberQ[#, n]&&Length[Select[Tuples[If[#==1, {}, First/@FactorInteger[#]]&/@#], UnsameQ@@#&]]>0&]], {n, 0, 10}]
CROSSREFS
Not requiring n gives A370585, maximal case of A370582, complement A370583.
Maximal case of A370586, complement A370587, unique A370588.
An opposite version is A370591.
A006530 gives greatest prime factor, least A020639.
A027746 lists prime factors, indices A112798, length A001222.
A355741 counts choices of a prime factor of each prime index.
A367902 counts choosable set-systems, ranks A367906, unlabeled A368095.
A367903 counts non-choosable set-systems, ranks A367907, unlabeled A368094.
A368098 counts choosable unlabeled multiset partitions, complement A368097.
A368100 ranks choosable multisets, complement A355529.
A368414 counts choosable factorizations, complement A368413.
A370592 counts choosable partitions, complement A370593.
Sequence in context: A138182 A167835 A102044 * A125766 A093870 A250445
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Feb 28 2024
STATUS
approved