cp's OEIS Frontend

A343655 Number of pairwise coprime sets of divisors of n, where a singleton is not considered pairwise coprime unless it is {1}.

%I A343655 #8 Apr 28 2021 20:44:26
%S A343655 1,2,2,3,2,6,2,4,3,6,2,10,2,6,6,5,2,10,2,10,6,6,2,14,3,6,4,10,2,22,2,
%T A343655 6,6,6,6,17,2,6,6,14,2,22,2,10,10,6,2,18,3,10,6,10,2,14,6,14,6,6,2,38,
%U A343655 2,6,10,7,6,22,2,10,6,22,2,24,2,6,10,10,6,22,2
%N A343655 Number of pairwise coprime sets of divisors of n, where a singleton is not considered pairwise coprime unless it is {1}.
%C A343655 First differs from A015995 at a(210) = 88, A015995(210) = 86.
%e A343655 For example, the a(n) subsets for n = 1, 2, 4, 6, 8, 12, 16, 24 are:
%e A343655   {1}  {1}    {1}    {1}      {1}    {1}      {1}     {1}
%e A343655        {1,2}  {1,2}  {1,2}    {1,2}  {1,2}    {1,2}   {1,2}
%e A343655               {1,4}  {1,3}    {1,4}  {1,3}    {1,4}   {1,3}
%e A343655                      {1,6}    {1,8}  {1,4}    {1,8}   {1,4}
%e A343655                      {2,3}           {1,6}    {1,16}  {1,6}
%e A343655                      {1,2,3}         {2,3}            {1,8}
%e A343655                                      {3,4}            {2,3}
%e A343655                                      {1,12}           {3,4}
%e A343655                                      {1,2,3}          {3,8}
%e A343655                                      {1,3,4}          {1,12}
%e A343655                                                       {1,24}
%e A343655                                                       {1,2,3}
%e A343655                                                       {1,3,4}
%e A343655                                                       {1,3,8}
%t A343655 Table[Length[Select[Subsets[Divisors[n]],CoprimeQ@@#&]],{n,100}]
%Y A343655 The case of pairs is A063647.
%Y A343655 The case of triples is A066620.
%Y A343655 The version with empty sets and singletons is A225520.
%Y A343655 A version for prime indices is A304711.
%Y A343655 The version for strict integer partitions is A305713.
%Y A343655 The version for subsets of {1..n} is A320426 = A276187 + 1.
%Y A343655 The version for binary indices is A326675.
%Y A343655 The version for integer partitions is A327516.
%Y A343655 The version for standard compositions is A333227.
%Y A343655 The maximal case is A343652.
%Y A343655 The case without 1's is A343653.
%Y A343655 The case without 1's with singletons is A343654.
%Y A343655 The maximal case without 1's is A343660.
%Y A343655 A018892 counts coprime unordered pairs of divisors.
%Y A343655 A051026 counts pairwise indivisible subsets of {1..n}.
%Y A343655 A100565 counts pairwise coprime unordered triples of divisors.
%Y A343655 A325683 counts maximal Golomb rulers.
%Y A343655 A326077 counts maximal pairwise indivisible sets.
%Y A343655 Cf. A007360, A062319, A067824, A076078, A084422, A187106, A282935, A285572, A304709, A320423, A337485, A343659.
%K A343655 nonn
%O A343655 1,2
%A A343655 _Gus Wiseman_, Apr 26 2021