cp's OEIS Frontend

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

%I A343654 #8 Apr 28 2021 07:41:25
%S A343654 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,
%T A343654 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,
%U A343654 5,15,2,8,5,15,2,18,2,5,8,8,5,15,2,14,5,5
%N A343654 Number of pairwise coprime sets of divisors > 1 of n.
%C A343654 First differs from A100565 at a(210) = 52, A100565(210) = 51.
%e A343654 The a(n) sets for n = 1, 2, 4, 6, 8, 12, 24, 30, 32, 36, 48:
%e A343654   {}  {}   {}   {}     {}   {}     {}     {}       {}    {}     {}
%e A343654       {2}  {2}  {2}    {2}  {2}    {2}    {2}      {2}   {2}    {2}
%e A343654            {4}  {3}    {4}  {3}    {3}    {3}      {4}   {3}    {3}
%e A343654                 {6}    {8}  {4}    {4}    {5}      {8}   {4}    {4}
%e A343654                 {2,3}       {6}    {6}    {6}      {16}  {6}    {6}
%e A343654                             {12}   {8}    {10}     {32}  {9}    {8}
%e A343654                             {2,3}  {12}   {15}           {12}   {12}
%e A343654                             {3,4}  {24}   {30}           {18}   {16}
%e A343654                                    {2,3}  {2,3}          {36}   {24}
%e A343654                                    {3,4}  {2,5}          {2,3}  {48}
%e A343654                                    {3,8}  {3,5}          {2,9}  {2,3}
%e A343654                                           {5,6}          {3,4}  {3,4}
%e A343654                                           {2,15}         {4,9}  {3,8}
%e A343654                                           {3,10}                {3,16}
%e A343654                                           {2,3,5}
%t A343654 pwcop[y_]:=And@@(GCD@@#1==1&)/@Subsets[y,{2}];
%t A343654 Table[Length[Select[Subsets[Rest[Divisors[n]]],pwcop]],{n,100}]
%Y A343654 The version for partitions is A007359.
%Y A343654 The version for subsets of {1..n} is A084422.
%Y A343654 The case of pairs is A089233.
%Y A343654 The version with 1's is A225520.
%Y A343654 The maximal case is A343652.
%Y A343654 The case without empty sets or singletons is A343653.
%Y A343654 The maximal case without singletons is A343660.
%Y A343654 A018892 counts pairwise coprime unordered pairs of divisors.
%Y A343654 A051026 counts pairwise indivisible subsets of {1..n}.
%Y A343654 A100565 counts pairwise coprime unordered triples of divisors.
%Y A343654 A187106, A276187, and A320426 count other types of pairwise coprime sets.
%Y A343654 A326077 counts maximal pairwise indivisible sets.
%Y A343654 Cf. A007360, A051026, A062319, A074206, A087087, A101268, A285572, A305713, A320423, A326675, A337485, A343655.
%K A343654 nonn
%O A343654 1,2
%A A343654 _Gus Wiseman_, Apr 26 2021