OFFSET

0,4

EXAMPLE

The a(0) = 0 through a(7) = 20 subsets:

. . {2} {3} {4} {5} {6} {7}

{2,3} {3,4} {2,5} {2,6} {2,7}

{3,5} {3,6} {3,7}

{4,5} {4,6} {4,7}

{2,3,5} {5,6} {5,7}

{3,4,5} {2,5,6} {6,7}

{3,5,6} {2,3,7}

{4,5,6} {2,5,7}

{2,6,7}

{3,4,7}

{3,5,7}

{3,6,7}

{4,5,7}

{4,6,7}

{5,6,7}

{2,3,5,7}

{2,5,6,7}

{3,4,5,7}

{3,5,6,7}

{4,5,6,7}

MATHEMATICA

Table[Length[Select[Subsets[Range[n]], MemberQ[#, n]&&Length[Select[Tuples[If[#==1, {}, First/@FactorInteger[#]]&/@#], UnsameQ@@#&]]>0&]], {n, 0, 10}]

CROSSREFS

Maximal choosable sets are counted by A370585.

The complement is counted by A370587.

For a unique choice we have A370588.

For binary indices instead of prime factors we have A370639.

A355741 counts choices of a prime factor of each prime index.

KEYWORD

nonn

AUTHOR

Gus Wiseman, Feb 26 2024

EXTENSIONS

a(19)-a(41) from Alois P. Heinz, Feb 27 2024

STATUS

approved