A326494 Number of subsets of {1..n} containing all differences and quotients of pairs of distinct elements.
1, 2, 4, 6, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127
Offset: 0
Keywords
Examples
The a(0) = 1 through a(6) = 13 subsets:
{} {} {} {} {} {} {}
{1} {1} {1} {1} {1} {1}
{2} {2} {2} {2} {2}
{1,2} {3} {3} {3} {3}
{1,2} {4} {4} {4}
{1,2,3} {1,2} {5} {5}
{2,4} {1,2} {6}
{1,2,3} {2,4} {1,2}
{1,2,3,4} {1,2,3} {2,4}
{1,2,3,4} {1,2,3}
{1,2,3,4,5} {1,2,3,4}
{1,2,3,4,5}
{1,2,3,4,5,6}
Crossrefs
Programs
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Mathematica
Table[Length[Select[Subsets[Range[n]],SubsetQ[#,Union[Divide@@@Select[Tuples[#,2],UnsameQ@@#&&Divisible@@#&],Subtract@@@Select[Tuples[#,2],Greater@@#&]]]&]],{n,0,10}]
Formula
a(n) = 2*n + 1 = A005408(n) for n > 3. - Andrew Howroyd, Aug 25 2019
Extensions
Terms a(20) and beyond from Andrew Howroyd, Aug 25 2019
Comments