A343653 Number of non-singleton pairwise coprime nonempty sets of divisors > 1 of n.

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 0, 0, 2, 0, 2, 1, 1, 0, 3, 0, 1, 0, 2, 0, 7, 0, 0, 1, 1, 1, 4, 0, 1, 1, 3, 0, 7, 0, 2, 2, 1, 0, 4, 0, 2, 1, 2, 0, 3, 1, 3, 1, 1, 0, 13, 0, 1, 2, 0, 1, 7, 0, 2, 1, 7, 0, 6, 0, 1, 2, 2, 1, 7, 0, 4, 0, 1, 0, 13, 1, 1

Offset

1,12

Comments

First differs from A066620 at a(210) = 36, A066620(210) = 35.

Links

Table of n, a(n) for n=1..86.

Example

The a(n) sets for n = 6, 12, 24, 30, 36, 60, 72, 96:
  {2,3}  {2,3}  {2,3}  {2,3}    {2,3}  {2,3}    {2,3}  {2,3}
         {3,4}  {3,4}  {2,5}    {2,9}  {2,5}    {2,9}  {3,4}
                {3,8}  {3,5}    {3,4}  {3,4}    {3,4}  {3,8}
                       {5,6}    {4,9}  {3,5}    {3,8}  {3,16}
                       {2,15}          {4,5}    {4,9}  {3,32}
                       {3,10}          {5,6}    {8,9}
                       {2,3,5}         {2,15}
                                       {3,10}
                                       {3,20}
                                       {4,15}
                                       {5,12}
                                       {2,3,5}
                                       {3,4,5}

Mathematica

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

Crossrefs

The case of pairs is A089233.

The version with 1's, empty sets, and singletons is A225520.

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

The version for strict partitions is A337485.

The version for compositions is A337697.

The version for prime indices is A337984.

The maximal case with 1's is A343652.

The version with empty sets is a(n) + 1.

The version with singletons is A343654(n) - 1.

The version with empty sets and singletons is A343654.

The version with 1's is A343655.

The maximal case is A343660.

A018892 counts pairwise coprime unordered pairs of divisors.

A048691 counts pairwise coprime ordered pairs of divisors.

A048785 counts pairwise coprime ordered triples of divisors.

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

A100565 counts pairwise coprime unordered triples of divisors.

A305713 counts pairwise coprime non-singleton strict partitions.

A343659 counts maximal pairwise coprime subsets of {1..n}.

Cf. A007359, A067824, A074206, A076078, A084422, A187106, A285572, A324837, A326675, A327516, A338315.

Sequence in context: A281116 A335447 A089233 * A066620 A219023 A025427

Adjacent sequences: A343650 A343651 A343652 * A343654 A343655 A343656

Keyword

nonn

Author

Gus Wiseman, Apr 25 2021

Status

approved