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

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, 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, 2, 6, 10, 7, 6, 22, 2, 10, 6, 22, 2, 24, 2, 6, 10, 10, 6, 22, 2

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..79.

Example

For example, the a(n) subsets for n = 1, 2, 4, 6, 8, 12, 16, 24 are:
  {1}  {1}    {1}    {1}      {1}    {1}      {1}     {1}
       {1,2}  {1,2}  {1,2}    {1,2}  {1,2}    {1,2}   {1,2}
              {1,4}  {1,3}    {1,4}  {1,3}    {1,4}   {1,3}
                     {1,6}    {1,8}  {1,4}    {1,8}   {1,4}
                     {2,3}           {1,6}    {1,16}  {1,6}
                     {1,2,3}         {2,3}            {1,8}
                                     {3,4}            {2,3}
                                     {1,12}           {3,4}
                                     {1,2,3}          {3,8}
                                     {1,3,4}          {1,12}
                                                      {1,24}
                                                      {1,2,3}
                                                      {1,3,4}
                                                      {1,3,8}

Mathematica

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

Crossrefs

The case of pairs is A063647.

The case of triples is A066620.

The version with empty sets and singletons is A225520.

A version for prime indices is A304711.

The version for strict integer partitions is A305713.

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

The version for binary indices is A326675.

The version for integer partitions is A327516.

The version for standard compositions is A333227.

The maximal case is A343652.

The case without 1's is A343653.

The case without 1's with singletons is A343654.

The maximal case without 1's is A343660.

A018892 counts coprime unordered pairs of divisors.

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

A100565 counts pairwise coprime unordered triples of divisors.

A325683 counts maximal Golomb rulers.

A326077 counts maximal pairwise indivisible sets.

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

Sequence in context: A378747 A199583 A157922 * A015995 A376567 A068903

Adjacent sequences: A343652 A343653 A343654 * A343656 A343657 A343658

Keyword

nonn

Author

Gus Wiseman, Apr 26 2021

Status

approved