OFFSET
0,2
COMMENTS
These sets are closed under taking the quotient of two distinct divisible terms.
EXAMPLE
The a(6) = 48 subsets:
{} {1} {1,2} {1,2,3} {1,2,3,4} {1,2,3,4,5} {1,2,3,4,5,6}
{2} {1,3} {1,2,4} {1,2,3,5} {1,2,3,4,6}
{3} {1,4} {1,2,5} {1,2,3,6} {1,2,3,5,6}
{4} {1,5} {1,3,4} {1,2,4,5} {2,3,4,5,6}
{5} {1,6} {1,3,5} {1,3,4,5}
{6} {2,3} {1,4,5} {1,4,5,6}
{2,4} {1,4,6} {2,3,4,5}
{2,5} {1,5,6} {2,3,4,6}
{3,4} {2,3,4} {2,3,5,6}
{3,5} {2,3,5}
{4,5} {2,3,6}
{4,6} {2,4,5}
{5,6} {3,4,5}
{4,5,6}
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], SubsetQ[#, Divide@@@Select[Tuples[#, 2], UnsameQ@@#&&Divisible@@#&]]&]], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 05 2019
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Aug 30 2019
STATUS
approved