A343653 - OEIS

%I #17 Aug 01 2021 01:56:30

%S 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,

%T 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,

%U 1,7,0,6,0,1,2,2,1,7,0,4,0,1,0,13,1,1

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

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

%e The a(n) sets for n = 6, 12, 24, 30, 36, 60, 72, 96:

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

%e          {3,4}  {3,4}  {2,5}    {2,9}  {2,5}    {2,9}  {3,4}

%e                 {3,8}  {3,5}    {3,4}  {3,4}    {3,4}  {3,8}

%e                        {5,6}    {4,9}  {3,5}    {3,8}  {3,16}

%e                        {2,15}          {4,5}    {4,9}  {3,32}

%e                        {3,10}          {5,6}    {8,9}

%e                        {2,3,5}         {2,15}

%e                                        {3,10}

%e                                        {3,20}

%e                                        {4,15}

%e                                        {5,12}

%e                                        {2,3,5}

%e                                        {3,4,5}

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

%Y The case of pairs is A089233.

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

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

%Y The version for strict partitions is A337485.

%Y The version for compositions is A337697.

%Y The version for prime indices is A337984.

%Y The maximal case with 1's is A343652.

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

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

%Y The version with empty sets and singletons is A343654.

%Y The version with 1's is A343655.

%Y The maximal case is A343660.

%Y A018892 counts pairwise coprime unordered pairs of divisors.

%Y A048691 counts pairwise coprime ordered pairs of divisors.

%Y A048785 counts pairwise coprime ordered triples of divisors.

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

%Y A100565 counts pairwise coprime unordered triples of divisors.

%Y A305713 counts pairwise coprime non-singleton strict partitions.

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

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

%K nonn

%O 1,12

%A _Gus Wiseman_, Apr 25 2021