cp's OEIS Frontend

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

%I A343653 #17 Aug 01 2021 01:56:30
%S A343653 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 A343653 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 A343653 1,7,0,6,0,1,2,2,1,7,0,4,0,1,0,13,1,1
%N A343653 Number of non-singleton pairwise coprime nonempty sets of divisors > 1 of n.
%C A343653 First differs from A066620 at a(210) = 36, A066620(210) = 35.
%e A343653 The a(n) sets for n = 6, 12, 24, 30, 36, 60, 72, 96:
%e A343653   {2,3}  {2,3}  {2,3}  {2,3}    {2,3}  {2,3}    {2,3}  {2,3}
%e A343653          {3,4}  {3,4}  {2,5}    {2,9}  {2,5}    {2,9}  {3,4}
%e A343653                 {3,8}  {3,5}    {3,4}  {3,4}    {3,4}  {3,8}
%e A343653                        {5,6}    {4,9}  {3,5}    {3,8}  {3,16}
%e A343653                        {2,15}          {4,5}    {4,9}  {3,32}
%e A343653                        {3,10}          {5,6}    {8,9}
%e A343653                        {2,3,5}         {2,15}
%e A343653                                        {3,10}
%e A343653                                        {3,20}
%e A343653                                        {4,15}
%e A343653                                        {5,12}
%e A343653                                        {2,3,5}
%e A343653                                        {3,4,5}
%t A343653 Table[Length[Select[Subsets[Rest[Divisors[n]]],CoprimeQ@@#&]],{n,100}]
%Y A343653 The case of pairs is A089233.
%Y A343653 The version with 1's, empty sets, and singletons is A225520.
%Y A343653 The version for subsets of {1..n} is A320426.
%Y A343653 The version for strict partitions is A337485.
%Y A343653 The version for compositions is A337697.
%Y A343653 The version for prime indices is A337984.
%Y A343653 The maximal case with 1's is A343652.
%Y A343653 The version with empty sets is a(n) + 1.
%Y A343653 The version with singletons is A343654(n) - 1.
%Y A343653 The version with empty sets and singletons is A343654.
%Y A343653 The version with 1's is A343655.
%Y A343653 The maximal case is A343660.
%Y A343653 A018892 counts pairwise coprime unordered pairs of divisors.
%Y A343653 A048691 counts pairwise coprime ordered pairs of divisors.
%Y A343653 A048785 counts pairwise coprime ordered triples of divisors.
%Y A343653 A051026 counts pairwise indivisible subsets of {1..n}.
%Y A343653 A100565 counts pairwise coprime unordered triples of divisors.
%Y A343653 A305713 counts pairwise coprime non-singleton strict partitions.
%Y A343653 A343659 counts maximal pairwise coprime subsets of {1..n}.
%Y A343653 Cf. A007359, A067824, A074206, A076078, A084422, A187106, A285572, A324837, A326675, A327516, A338315.
%K A343653 nonn
%O A343653 1,12
%A A343653 _Gus Wiseman_, Apr 25 2021