A326025 Number of maximal subsets of {1..n} containing no sums or products of distinct elements.

1, 1, 2, 2, 2, 4, 5, 10, 13, 20, 28, 40, 54, 82, 120, 172, 244, 347, 471, 651, 874, 1198, 1635, 2210, 2867, 3895, 5234, 6889, 9019, 11919, 15629, 20460, 26254, 33827, 43881, 56367, 71841, 91834, 117695, 148503, 188039, 311442, 390859, 488327, 610685, 759665

Offset

0,3

Links

Table of n, a(n) for n=0..45.

Andrew Howroyd, PARI Program

Example

The a(1) = 1 through a(8) = 13 maximal subsets:
  {1}  {1}  {1}    {1}      {1}      {1}        {1}        {1}
       {2}  {2,3}  {2,3,4}  {2,3,4}  {2,3,4}    {2,3,4}    {2,3,4}
                            {2,4,5}  {2,4,5}    {2,3,7}    {2,4,5}
                            {3,4,5}  {2,5,6}    {2,4,5}    {2,4,7}
                                     {3,4,5,6}  {2,4,7}    {2,5,6}
                                                {2,5,6}    {2,5,8}
                                                {2,6,7}    {2,6,7}
                                                {3,4,5,6}  {2,3,7,8}
                                                {3,5,6,7}  {3,4,5,6}
                                                {4,5,6,7}  {3,4,6,8}
                                                           {3,5,6,7}
                                                           {3,6,7,8}
                                                           {4,5,6,7,8}

Mathematica

fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]], Intersection[#, Union[Plus@@@Subsets[#, {2, n}], Times@@@Subsets[#, {2, n}]]]=={}&]]], {n, 0, 10}]

Prog

(PARI) \\ See link for program file.
for(n=0, 25, print1(A326025(n), ", ")) \\ Andrew Howroyd, Aug 29 2019

Crossrefs

Maximal subsets without sums of distinct elements are A326498.

Maximal subsets without products of distinct elements are A325710.

Subsets without sums or products of distinct elements are A326024.

Subsets with sums (and products) are A326083.

Maximal sum-free and product-free subsets are A326497.

Cf. A007865, A051026, A121269, A151897, A326116, A326117, A326491, A326495, A326496.

Sequence in context: A230381 A082547 A068928 * A278502 A278501 A278231

Adjacent sequences: A326022 A326023 A326024 * A326026 A326027 A326028

Keyword

nonn

Author

Gus Wiseman, Jul 09 2019

Extensions

a(16)-a(40) from Andrew Howroyd, Aug 29 2019

a(41)-a(45) from Jinyuan Wang, Oct 03 2020

Status

approved