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A326023
Number of subsets of {1..n} containing all of their integer quotients.
19
1, 2, 3, 5, 9, 17, 25, 49, 73, 145, 217, 433, 553, 1105, 1657, 2593, 3937, 7873, 10057, 20113, 26689, 42321, 63481, 126961, 154801, 309601, 464401, 737569, 992161, 1984321, 2450881, 4901761, 6292801, 10197313, 15295969, 26241697, 32947489, 65894977, 98842465, 161587873, 205842529
OFFSET
0,2
COMMENTS
These are sets that are closed under taking the quotient of two (not necessarily distinct) divisible terms.
FORMULA
For n > 0, a(n) = A326078(n) + 1.
EXAMPLE
The a(0) = 1 through a(5) = 17 subsets:
{} {} {} {} {} {}
{1} {1} {1} {1} {1}
{1,2} {1,2} {1,2} {1,2}
{1,3} {1,3} {1,3}
{1,2,3} {1,4} {1,4}
{1,2,3} {1,5}
{1,2,4} {1,2,3}
{1,3,4} {1,2,4}
{1,2,3,4} {1,2,5}
{1,3,4}
{1,3,5}
{1,4,5}
{1,2,3,4}
{1,2,3,5}
{1,2,4,5}
{1,3,4,5}
{1,2,3,4,5}
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], SubsetQ[#, Select[Divide@@@Tuples[#, 2], IntegerQ]]&]], {n, 0, 10}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 04 2019
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Aug 30 2019
STATUS
approved