cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A325710 Number of maximal subsets of {1..n} containing no products of distinct elements.

Original entry on oeis.org

1, 1, 2, 2, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 24, 28, 32, 32, 62, 62, 92, 102, 184, 184, 254, 254, 474, 506, 686, 686, 1172, 1172, 1792, 1906, 3568, 3794, 5326, 5326, 10282, 10618, 14822, 14822, 25564, 25564, 35304, 39432, 76888, 76888, 100574, 100574, 197870, 201622, 282014
Offset: 0

Views

Author

Gus Wiseman, Jul 09 2019

Keywords

Examples

			The a(1) = 1 through a(9) = 6 maximal subsets:
  {1}  {1}  {1}   {1}    {1}     {1}     {1}      {1}       {1}
       {2}  {23}  {234}  {2345}  {2345}  {23457}  {23457}   {234579}
                                 {2456}  {24567}  {23578}   {235789}
                                 {3456}  {34567}  {24567}   {245679}
                                                  {25678}   {256789}
                                                  {345678}  {3456789}

Links

Crossrefs

Subsets without products of distinct elements are A326117.
Maximal product-free subsets are A326496.
Subsets with products are A326076.
Maximal subsets without sums of distinct elements are A326498.
Maximal subsets without quotients are A326492.
Maximal subsets without sums or products of distinct elements are A326025.
Cf. A121269, A151897, A326116, A326489, A326497, A326024.

Programs

  • Mathematica
    fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,Times@@@Subsets[#,{2,n}]]=={}&]]],{n,0,10}]
  • PARI
    \\ See link for program file.
for(n=0, 30, print1(A325710(n), ", ")) \\ Andrew Howroyd, Aug 29 2019

Extensions

Terms a(16) and beyond from Andrew Howroyd, Aug 29 2019

A326498 Number of maximal subsets of {1..n} containing no sums of distinct elements.

Original entry on oeis.org

1, 1, 1, 3, 3, 6, 11, 16, 20, 32, 53, 78, 107, 149, 206, 292, 391, 556, 782, 1062, 1451, 1929, 2564, 3404, 4431, 5853, 7672, 9999, 12973, 16922, 22194, 28655, 36734, 47036, 60375, 76866, 97892, 123627, 157008, 196633, 248221, 311442, 390859, 488327, 610685
Offset: 0

Views

Author

Gus Wiseman, Jul 09 2019

Keywords

Examples

			The a(1) = 1 through a(7) = 16 subsets:
  {1}  {1,2}  {1,2}  {1,3}    {1,2,4}  {1,2,4}    {1,2,4}
              {1,3}  {1,2,4}  {1,2,5}  {1,2,5}    {1,2,5}
              {2,3}  {2,3,4}  {1,3,5}  {1,2,6}    {1,2,6}
                              {2,3,4}  {1,3,5}    {1,2,7}
                              {2,4,5}  {1,3,6}    {1,3,6}
                              {3,4,5}  {1,4,6}    {1,4,6}
                                       {2,3,4}    {1,4,7}
                                       {2,3,6}    {2,3,4}
                                       {2,4,5}    {2,4,5}
                                       {2,5,6}    {2,4,7}
                                       {3,4,5,6}  {2,5,6}
                                                  {1,3,5,7}
                                                  {2,3,6,7}
                                                  {3,4,5,6}
                                                  {3,5,6,7}
                                                  {4,5,6,7}

Links

Crossrefs

Subsets without sums of distinct elements are A151897.
Maximal sum-free subsets are A121269.
Subsets with sums are A326083.
Maximal subsets without products of distinct elements are A325710.
Maximal subsets without sums or products of distinct elements are A326025.
Cf. A007865, A103580, A326117, A326495, A326497.

Programs

  • Mathematica
    fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]],Intersection[#,Plus@@@Subsets[#,{2,n}]]=={}&]]],{n,0,10}]
  • PARI
    \\ See link for program file.
for(n=0, 25, print1(A326498(n), ", ")) \\ Andrew Howroyd, Aug 29 2019

Extensions

a(16)-a(40) from Andrew Howroyd, Aug 29 2019
a(41)-a(44) from Jinyuan Wang, Oct 11 2020

A326024 Number of subsets of {1..n} containing no sums or products of distinct elements.

Original entry on oeis.org

1, 2, 3, 5, 9, 15, 25, 41, 68, 109, 179, 284, 443, 681, 1062, 1587, 2440, 3638, 5443, 8021, 11953, 17273, 25578, 37001, 53953, 77429, 113063, 160636, 232928, 330775, 475380, 672056, 967831, 1359743, 1952235, 2743363, 3918401, 5495993, 7856134, 10984547, 15669741
Offset: 0

Views

Author

Gus Wiseman, Jul 09 2019

Keywords

Examples

			The a(0) = 1 through a(5) = 15 subsets:
  {}  {}   {}   {}     {}       {}
      {1}  {1}  {1}    {1}      {1}
           {2}  {2}    {2}      {2}
                {3}    {3}      {3}
                {2,3}  {4}      {4}
                       {2,3}    {5}
                       {2,4}    {2,3}
                       {3,4}    {2,4}
                       {2,3,4}  {2,5}
                                {3,4}
                                {3,5}
                                {4,5}
                                {2,3,4}
                                {2,4,5}
                                {3,4,5}

Links

Crossrefs

Subsets without sums of distinct elements are A151897.
Subsets without products of distinct elements are A326117.
Maximal subsets without sums or products of distinct elements are A326025.
Subsets with sums (and products) are A326083.
Sum-free and product-free subsets are A326495.
Cf. A007865, A051026, A121269, A325710, A326076, A326489, A326497, A326498.

Programs

  • Mathematica
    Table[Length[Select[Subsets[Range[n]],Intersection[#,Union[Plus@@@Subsets[#,{2,n}],Times@@@Subsets[#,{2,n}]]]=={}&]],{n,0,10}]
  • PARI
    a(n)={
   my(recurse(k, es, ep)=
    if(k > n, 1,
      my(t = self()(k + 1, es, ep));
      if(!bittest(es,k) && !bittest(ep,k),
         es = bitor(es, bitand((2<Andrew Howroyd, Aug 25 2019

Extensions

Terms a(16)-a(40) from Andrew Howroyd, Aug 25 2019
Showing 1-3 of 3 results.

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