A343655 - OEIS

%I #8 Apr 28 2021 20:44:26

%S 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 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 2,6,10,7,6,22,2,10,6,22,2,24,2,6,10,10,6,22,2

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

%C First differs from A015995 at a(210) = 88, A015995(210) = 86.

%e For example, the a(n) subsets for n = 1, 2, 4, 6, 8, 12, 16, 24 are:

%e   {1}  {1}    {1}    {1}      {1}    {1}      {1}     {1}

%e        {1,2}  {1,2}  {1,2}    {1,2}  {1,2}    {1,2}   {1,2}

%e               {1,4}  {1,3}    {1,4}  {1,3}    {1,4}   {1,3}

%e                      {1,6}    {1,8}  {1,4}    {1,8}   {1,4}

%e                      {2,3}           {1,6}    {1,16}  {1,6}

%e                      {1,2,3}         {2,3}            {1,8}

%e                                      {3,4}            {2,3}

%e                                      {1,12}           {3,4}

%e                                      {1,2,3}          {3,8}

%e                                      {1,3,4}          {1,12}

%e                                                       {1,24}

%e                                                       {1,2,3}

%e                                                       {1,3,4}

%e                                                       {1,3,8}

%t Table[Length[Select[Subsets[Divisors[n]],CoprimeQ@@#&]],{n,100}]

%Y The case of pairs is A063647.

%Y The case of triples is A066620.

%Y The version with empty sets and singletons is A225520.

%Y A version for prime indices is A304711.

%Y The version for strict integer partitions is A305713.

%Y The version for subsets of {1..n} is A320426 = A276187 + 1.

%Y The version for binary indices is A326675.

%Y The version for integer partitions is A327516.

%Y The version for standard compositions is A333227.

%Y The maximal case is A343652.

%Y The case without 1's is A343653.

%Y The case without 1's with singletons is A343654.

%Y The maximal case without 1's is A343660.

%Y A018892 counts coprime unordered pairs of divisors.

%Y A051026 counts pairwise indivisible subsets of {1..n}.

%Y A100565 counts pairwise coprime unordered triples of divisors.

%Y A325683 counts maximal Golomb rulers.

%Y A326077 counts maximal pairwise indivisible sets.

%Y Cf. A007360, A062319, A067824, A076078, A084422, A187106, A282935, A285572, A304709, A320423, A337485, A343659.

%K nonn

%O 1,2

%A _Gus Wiseman_, Apr 26 2021