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A343652 Number of maximal pairwise coprime sets of divisors of n.

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%I A343652 #16 Apr 28 2021 07:41:16
%S A343652 1,1,1,2,1,2,1,3,2,2,1,4,1,2,2,4,1,4,1,4,2,2,1,6,2,2,3,4,1,5,1,5,2,2,
%T A343652 2,8,1,2,2,6,1,5,1,4,4,2,1,8,2,4,2,4,1,6,2,6,2,2,1,10,1,2,4,6,2,5,1,4,
%U A343652 2,5,1,12,1,2,4,4,2,5,1,8,4,2,1,10,2,2
%N A343652 Number of maximal pairwise coprime sets of divisors of n.
%C A343652 Also the number of maximal pairwise coprime sets of divisors > 1 of n. For example, the a(n) sets for n = 12, 30, 36, 60, 120 are:
%C A343652   {6}    {30}     {6}    {30}     {30}
%C A343652   {12}   {2,15}   {12}   {60}     {60}
%C A343652   {2,3}  {3,10}   {18}   {2,15}   {120}
%C A343652   {3,4}  {5,6}    {36}   {3,10}   {2,15}
%C A343652          {2,3,5}  {2,3}  {3,20}   {3,10}
%C A343652                   {2,9}  {4,15}   {3,20}
%C A343652                   {3,4}  {5,6}    {3,40}
%C A343652                   {4,9}  {5,12}   {4,15}
%C A343652                          {2,3,5}  {5,6}
%C A343652                          {3,4,5}  {5,12}
%C A343652                                   {5,24}
%C A343652                                   {8,15}
%C A343652                                   {2,3,5}
%C A343652                                   {3,4,5}
%C A343652                                   {3,5,8}
%F A343652 a(n) = A343660(n) + A005361(n).
%e A343652 The a(n) sets for n = 12, 30, 36, 60, 120:
%e A343652   {1,6}    {1,30}     {1,6}    {1,30}     {1,30}
%e A343652   {1,12}   {1,2,15}   {1,12}   {1,60}     {1,60}
%e A343652   {1,2,3}  {1,3,10}   {1,18}   {1,2,15}   {1,120}
%e A343652   {1,3,4}  {1,5,6}    {1,36}   {1,3,10}   {1,2,15}
%e A343652            {1,2,3,5}  {1,2,3}  {1,3,20}   {1,3,10}
%e A343652                       {1,2,9}  {1,4,15}   {1,3,20}
%e A343652                       {1,3,4}  {1,5,6}    {1,3,40}
%e A343652                       {1,4,9}  {1,5,12}   {1,4,15}
%e A343652                                {1,2,3,5}  {1,5,6}
%e A343652                                {1,3,4,5}  {1,5,12}
%e A343652                                           {1,5,24}
%e A343652                                           {1,8,15}
%e A343652                                           {1,2,3,5}
%e A343652                                           {1,3,4,5}
%e A343652                                           {1,3,5,8}
%t A343652 fasmax[y_]:=Complement[y,Union@@Most@*Subsets/@y];
%t A343652 Table[Length[fasmax[Select[Subsets[Divisors[n]],CoprimeQ@@#&]]],{n,100}]
%Y A343652 The case of pairs is A063647.
%Y A343652 The case of triples is A066620.
%Y A343652 The non-maximal version counting empty sets and singletons is A225520.
%Y A343652 The non-maximal version with no 1's is A343653.
%Y A343652 The non-maximal version is A343655.
%Y A343652 The version for subsets of {1..n} is A343659.
%Y A343652 The case without 1's or singletons is A343660.
%Y A343652 A018892 counts pairwise coprime unordered pairs of divisors.
%Y A343652 A048691 counts pairwise coprime ordered pairs of divisors.
%Y A343652 A048785 counts pairwise coprime ordered triples of divisors.
%Y A343652 A084422, A187106, A276187, and A320426 count pairwise coprime sets.
%Y A343652 A100565 counts pairwise coprime unordered triples of divisors.
%Y A343652 A305713 counts pairwise coprime non-singleton strict partitions.
%Y A343652 A324837 counts minimal subsets of {1...n} with least common multiple n.
%Y A343652 A325683 counts maximal Golomb rulers.
%Y A343652 A326077 counts maximal pairwise indivisible sets.
%Y A343652 Cf. A005361, A007359, A051026, A062319, A067824, A074206, A146291, A285572, A325859, A326359, A326496, A326675, A343654.
%K A343652 nonn
%O A343652 1,4
%A A343652 _Gus Wiseman_, Apr 25 2021