cp's OEIS Frontend

A320426 Number of nonempty pairwise coprime subsets of {1,...,n}, where a single number is not considered to be pairwise coprime unless it is equal to 1.

%I A320426 #24 May 10 2021 23:30:34
%S A320426 1,2,5,8,19,22,49,64,95,106,221,236,483,530,601,712,1439,1502,3021,
%T A320426 3212,3595,3850,7721,7976,11143,11878,14629,15460,30947,31202,62433,
%U A320426 69856,76127,80222,89821,91612,183259,192602,208601,214232,428503,431574,863189
%N A320426 Number of nonempty pairwise coprime subsets of {1,...,n}, where a single number is not considered to be pairwise coprime unless it is equal to 1.
%C A320426 Two or more numbers are pairwise coprime if no pair of them has a common divisor > 1.
%F A320426 a(n) = A187106(n) - n + 1 = A084422(n) - n.
%F A320426 a(n) = A276187(n) + 1. - _Gus Wiseman_, May 08 2021
%e A320426 The a(4) = 8 subsets of {1,2,3,4} are {1}, {1,2}, {1,3}, {1,4}, {2,3}, {3,4}, {1,2,3}, {1,3,4}. - _Michael B. Porter_, Jan 12 2019
%e A320426 From _Gus Wiseman_, May 09 2021: (Start)
%e A320426 The a(2) = 2 through a(6) = 22 sets:
%e A320426    {1}     {1}      {1}       {1}        {1}
%e A320426   {1,2}   {1,2}    {1,2}     {1,2}      {1,2}
%e A320426           {1,3}    {1,3}     {1,3}      {1,3}
%e A320426           {2,3}    {1,4}     {1,4}      {1,4}
%e A320426          {1,2,3}   {2,3}     {1,5}      {1,5}
%e A320426                    {3,4}     {2,3}      {1,6}
%e A320426                   {1,2,3}    {2,5}      {2,3}
%e A320426                   {1,3,4}    {3,4}      {2,5}
%e A320426                              {3,5}      {3,4}
%e A320426                              {4,5}      {3,5}
%e A320426                             {1,2,3}     {4,5}
%e A320426                             {1,2,5}     {5,6}
%e A320426                             {1,3,4}    {1,2,3}
%e A320426                             {1,3,5}    {1,2,5}
%e A320426                             {1,4,5}    {1,3,4}
%e A320426                             {2,3,5}    {1,3,5}
%e A320426                             {3,4,5}    {1,4,5}
%e A320426                            {1,2,3,5}   {1,5,6}
%e A320426                            {1,3,4,5}   {2,3,5}
%e A320426                                        {3,4,5}
%e A320426                                       {1,2,3,5}
%e A320426                                       {1,3,4,5}
%e A320426 (End)
%t A320426 Table[Length[Select[Subsets[Range[n]],CoprimeQ@@#&]],{n,10}]
%Y A320426 The case of pairs is A015614.
%Y A320426 The case with singletons is A187106.
%Y A320426 The version without singletons (except {1}) is A276187.
%Y A320426 Row sums of A320436.
%Y A320426 The version for divisors > 1 is A343654.
%Y A320426 The version for divisors without singletons is A343655.
%Y A320426 The maximal version is A343659.
%Y A320426 A018892 counts coprime unordered pairs of divisors.
%Y A320426 A051026 counts pairwise indivisible subsets of {1...n}.
%Y A320426 A087087 ranks pairwise coprime subsets of {1...n}.
%Y A320426 A326675 ranks pairwise coprime non-singleton subsets of {1...n}.
%Y A320426 Cf. A007359, A007360, A066620, A089233, A100565, A225520, A325683, A326359, A337485, A343652.
%K A320426 nonn
%O A320426 1,2
%A A320426 _Gus Wiseman_, Jan 08 2019
%E A320426 a(25)-a(43) from _Alois P. Heinz_, Jan 08 2019