cp's OEIS Frontend

A326489 Number of product-free subsets of {1..n}.

%I A326489 #40 Jun 27 2022 23:34:34
%S A326489 1,1,2,4,6,12,22,44,88,136,252,504,896,1792,3392,6352,9720,19440,
%T A326489 35664,71328,129952,247232,477664,955328,1700416,2657280,5184000,
%U A326489 10368000,19407360,38814720,68868352,137736704,260693504,505830400,999641600,1882820608,2807196672
%N A326489 Number of product-free subsets of {1..n}.
%C A326489 A set is product-free if it contains no product of two (not necessarily distinct) elements.
%H A326489 Fausto A. C. Cariboni, <a href="/A326489/b326489.txt">Table of n, a(n) for n = 0..167</a>, (terms up to a(100) from Andrew Howroyd)
%H A326489 Marcel K. Goh and Jonah Saks, <a href="https://arxiv.org/abs/2206.12535">Alternating-sum statistics for certain sets of integers</a>, arXiv:2206.12535 [math.CO], 2022.
%H A326489 Andrew Howroyd, <a href="/A326489/a326489.txt">PARI Program</a>
%e A326489 The a(0) = 1 through a(6) = 22 subsets:
%e A326489   {}  {}  {}   {}     {}     {}       {}
%e A326489           {2}  {2}    {2}    {2}      {2}
%e A326489                {3}    {3}    {3}      {3}
%e A326489                {2,3}  {4}    {4}      {4}
%e A326489                       {2,3}  {5}      {5}
%e A326489                       {3,4}  {2,3}    {6}
%e A326489                              {2,5}    {2,3}
%e A326489                              {3,4}    {2,5}
%e A326489                              {3,5}    {2,6}
%e A326489                              {4,5}    {3,4}
%e A326489                              {2,3,5}  {3,5}
%e A326489                              {3,4,5}  {3,6}
%e A326489                                       {4,5}
%e A326489                                       {4,6}
%e A326489                                       {5,6}
%e A326489                                       {2,3,5}
%e A326489                                       {2,5,6}
%e A326489                                       {3,4,5}
%e A326489                                       {3,4,6}
%e A326489                                       {3,5,6}
%e A326489                                       {4,5,6}
%e A326489                                       {3,4,5,6}
%t A326489 Table[Length[Select[Subsets[Range[n]],Intersection[#,Times@@@Tuples[#,2]]=={}&]],{n,10}]
%Y A326489 Product-closed subsets are A326076.
%Y A326489 Subsets containing no products are A326114.
%Y A326489 Subsets containing no products of distinct elements are A326117.
%Y A326489 Subsets containing no quotients are A327591.
%Y A326489 Maximal product-free subsets are A326496.
%Y A326489 Cf. A007865, A051026, A326023, A326081, A326116, A326495.
%K A326489 nonn
%O A326489 0,3
%A A326489 _Gus Wiseman_, Jul 09 2019
%E A326489 a(21)-a(36) from _Andrew Howroyd_, Aug 25 2019
%E A326489 a(0)=1 prepended to data, example and b-file by _Peter Kagey_, Sep 18 2019