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A326494 Number of subsets of {1..n} containing all differences and quotients of pairs of distinct elements. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The only allowed sets are the empty set, any singleton, any initial interval of positive integers and {2,4}. This can be shown by induction. - Andrew Howroyd, Aug 25 2019

LINKS

Table of n, a(n) for n=0..63.

FORMULA

a(n) = 2*n + 1 = A005408(n) for n > 3. - Andrew Howroyd, Aug 25 2019

EXAMPLE

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}

MATHEMATICA

Table[Length[Select[Subsets[Range[n]], SubsetQ[#, Union[Divide@@@Select[Tuples[#, 2], UnsameQ@@#&&Divisible@@#&], Subtract@@@Select[Tuples[#, 2], Greater@@#&]]]&]], {n, 0, 10}]

CROSSREFS

Subsets with difference are A054519.

Subsets with quotients are A326023.

Subsets with quotients > 1 are A326079.

Subsets without differences or quotients are A326490.

Cf. A005408, A007865, A051026, A325849, A326076, A326491.

Sequence in context: A024978 A191194 A191231 * A285593 A248898 A207188

Adjacent sequences:  A326491 A326492 A326493 * A326495 A326496 A326497

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 09 2019

EXTENSIONS

Terms a(20) and beyond from Andrew Howroyd, Aug 25 2019

STATUS

approved

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Last modified September 21 12:49 EDT 2020. Contains 337272 sequences. (Running on oeis4.)