A364841 - OEIS

%I #10 Oct 18 2023 04:54:16

%S 1,2,3,6,9,15,21,34,49,75,105

%N 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 The a(0) = 1 through a(5) = 15 subsets:

%e   {}  {}   {}   {}     {}     {}

%e       {1}  {1}  {1}    {1}    {1}

%e            {2}  {2}    {2}    {2}

%e                 {3}    {3}    {3}

%e                 {1,3}  {4}    {4}

%e                 {2,3}  {1,3}  {5}

%e                        {1,4}  {1,3}

%e                        {2,3}  {1,4}

%e                        {3,4}  {1,5}

%e                               {2,3}

%e                               {2,5}

%e                               {3,4}

%e                               {3,5}

%e                               {4,5}

%e                               {3,4,5}

%t Table[Length[Select[Subsets[Range[n]], Intersection[#,Join@@Table[Total/@Tuples[#,k], {k,2,Length[#]}]]=={}&]],{n,0,10}]

%Y Cf. A007865, A085489, A103580, A151897, A236912, A326020, A326080, A326083, A364349, A364534.

%K nonn,more

%O 0,2

%A _Gus Wiseman_, Aug 15 2023