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A326079
Number of subsets of {1..n} containing all of their integer quotients > 1.
11
1, 2, 4, 8, 16, 32, 48, 96, 144, 288, 432, 864, 1104, 2208, 3312, 5184, 7872, 15744, 20112, 40224, 53376, 84640, 126960, 253920, 309600, 619200, 928800, 1475136, 1984320, 3968640, 4901760, 9803520, 12585600, 20394624, 30591936, 52483392, 65894976, 131789952, 197684928, 323175744, 411685056
OFFSET
0,2
COMMENTS
These sets are closed under taking the quotient of two distinct divisible terms.
FORMULA
For n > 0, a(n) = 2 * A326078(n) = 2 * (A326023(n) - 1).
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 05 2019
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Aug 30 2019
STATUS
approved