A343660 - OEIS

%I #11 Apr 28 2021 20:44:43

%S 0,0,0,0,0,1,0,0,0,1,0,2,0,1,1,0,0,2,0,2,1,1,0,3,0,1,0,2,0,4,0,0,1,1,

%T 1,4,0,1,1,3,0,4,0,2,2,1,0,4,0,2,1,2,0,3,1,3,1,1,0,8,0,1,2,0,1,4,0,2,

%U 1,4,0,6,0,1,2,2,1,4,0,4,0,1,0,8,1,1,1

%N Number of maximal pairwise coprime sets of at least two divisors > 1 of n.

%F a(n) = A343652(n) - A005361(n).

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

%e   {2,3}  {2,3}  {2,3}  {5,6}    {2,3}  {5,6}    {2,3}  {2,3}

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

%e                 {3,8}  {3,10}   {3,4}  {3,10}   {3,4}  {3,8}

%e                        {2,3,5}  {4,9}  {3,20}   {3,8}  {3,16}

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

%e                                        {5,12}   {8,9}

%e                                        {2,3,5}

%e                                        {3,4,5}

%t fasmax[y_]:=Complement[y,Union@@Most@*Subsets/@y];

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

%Y The case of pairs is A089233.

%Y The case with 1's is A343652.

%Y The case with singletons is (also) A343652.

%Y The non-maximal version is A343653.

%Y The non-maximal version with 1's is A343655.

%Y The version for subsets of {2..n} is A343659 (for n > 2).

%Y A018892 counts coprime unordered pairs of divisors.

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

%Y A066620 counts pairwise coprime 3-sets of divisors.

%Y A100565 counts pairwise coprime unordered triples of divisors.

%Y Cf. A005361, A007359, A007360, A067824, A074206, A225520, A276187, A320426, A325683, A326077, A326359, A326496, A337485, A343654.

%K nonn

%O 1,12

%A _Gus Wiseman_, Apr 26 2021