A343654 Number of pairwise coprime sets of divisors > 1 of n.

1, 2, 2, 3, 2, 5, 2, 4, 3, 5, 2, 8, 2, 5, 5, 5, 2, 8, 2, 8, 5, 5, 2, 11, 3, 5, 4, 8, 2, 15, 2, 6, 5, 5, 5, 13, 2, 5, 5, 11, 2, 15, 2, 8, 8, 5, 2, 14, 3, 8, 5, 8, 2, 11, 5, 11, 5, 5, 2, 25, 2, 5, 8, 7, 5, 15, 2, 8, 5, 15, 2, 18, 2, 5, 8, 8, 5, 15, 2, 14, 5, 5

Offset

1,2

Comments

First differs from A100565 at a(210) = 52, A100565(210) = 51.

Links

Table of n, a(n) for n=1..82.

Example

The a(n) sets for n = 1, 2, 4, 6, 8, 12, 24, 30, 32, 36, 48:
  {}  {}   {}   {}     {}   {}     {}     {}       {}    {}     {}
      {2}  {2}  {2}    {2}  {2}    {2}    {2}      {2}   {2}    {2}
           {4}  {3}    {4}  {3}    {3}    {3}      {4}   {3}    {3}
                {6}    {8}  {4}    {4}    {5}      {8}   {4}    {4}
                {2,3}       {6}    {6}    {6}      {16}  {6}    {6}
                            {12}   {8}    {10}     {32}  {9}    {8}
                            {2,3}  {12}   {15}           {12}   {12}
                            {3,4}  {24}   {30}           {18}   {16}
                                   {2,3}  {2,3}          {36}   {24}
                                   {3,4}  {2,5}          {2,3}  {48}
                                   {3,8}  {3,5}          {2,9}  {2,3}
                                          {5,6}          {3,4}  {3,4}
                                          {2,15}         {4,9}  {3,8}
                                          {3,10}                {3,16}
                                          {2,3,5}

Mathematica

pwcop[y_]:=And@@(GCD@@#1==1&)/@Subsets[y, {2}];
Table[Length[Select[Subsets[Rest[Divisors[n]]], pwcop]], {n, 100}]

Crossrefs

The version for partitions is A007359.

The version for subsets of {1..n} is A084422.

The case of pairs is A089233.

The version with 1's is A225520.

The maximal case is A343652.

The case without empty sets or singletons is A343653.

The maximal case without singletons is A343660.

A018892 counts pairwise coprime unordered pairs of divisors.

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

A100565 counts pairwise coprime unordered triples of divisors.

A187106, A276187, and A320426 count other types of pairwise coprime sets.

A326077 counts maximal pairwise indivisible sets.

Cf. A007360, A051026, A062319, A074206, A087087, A101268, A285572, A305713, A320423, A326675, A337485, A343655.

Sequence in context: A378436 A337331 A018892 * A100565 A244098 A285573

Adjacent sequences: A343651 A343652 A343653 * A343655 A343656 A343657

Keyword

nonn

Author

Gus Wiseman, Apr 26 2021

Status

approved