cp's OEIS Frontend

A364841 Number of subsets S of {1..n} containing no element equal to the sum of a k-multiset of elements of S, for any 2 <= k <= |S|.

%I A364841 #10 Oct 18 2023 04:54:16
%S A364841 1,2,3,6,9,15,21,34,49,75,105
%N A364841 Number of subsets S of {1..n} containing no element equal to the sum of a k-multiset of elements of S, for any 2 <= k <= |S|.
%e A364841 The a(0) = 1 through a(5) = 15 subsets:
%e A364841   {}  {}   {}   {}     {}     {}
%e A364841       {1}  {1}  {1}    {1}    {1}
%e A364841            {2}  {2}    {2}    {2}
%e A364841                 {3}    {3}    {3}
%e A364841                 {1,3}  {4}    {4}
%e A364841                 {2,3}  {1,3}  {5}
%e A364841                        {1,4}  {1,3}
%e A364841                        {2,3}  {1,4}
%e A364841                        {3,4}  {1,5}
%e A364841                               {2,3}
%e A364841                               {2,5}
%e A364841                               {3,4}
%e A364841                               {3,5}
%e A364841                               {4,5}
%e A364841                               {3,4,5}
%t A364841 Table[Length[Select[Subsets[Range[n]], Intersection[#,Join@@Table[Total/@Tuples[#,k], {k,2,Length[#]}]]=={}&]],{n,0,10}]
%Y A364841 Cf. A007865, A085489, A103580, A151897, A236912, A326020, A326080, A326083, A364349, A364534.
%K A364841 nonn,more
%O A364841 0,2
%A A364841 _Gus Wiseman_, Aug 15 2023