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

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

0,3

Links

Table of n, a(n) for n=0..52.

Andrew Howroyd, PARI Program

Example

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}

Mathematica

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

Prog

(PARI) \\ See link for program file.
for(n=0, 30, print1(A325710(n), ", ")) \\ Andrew Howroyd, Aug 29 2019

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.

Sequence in context: A347325 A324762 A104976 * A214927 A326115 A355746

Adjacent sequences: A325707 A325708 A325709 * A325711 A325712 A325713

Keyword

nonn

Author

Gus Wiseman, Jul 09 2019

Extensions

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

Status

approved