cp's OEIS Frontend

A308542 Number of subsets of {2..n} containing the product of any set of distinct elements whose product is <= n.

%I A308542 #8 Aug 25 2019 19:44:03
%S A308542 1,2,4,8,16,28,56,100,200,364,728,1184,2368,4448,8056,15008,30016,
%T A308542 52736,105472,183424,339840,663616,1327232,2217088,4434176,8744320,
%U A308542 16559168,30034624,60069248,103402112,206804224,379941440,730800064,1454649248,2659869664,4786282208
%N A308542 Number of subsets of {2..n} containing the product of any set of distinct elements whose product is <= n.
%C A308542 First differs from A326116 at a(12) = 1184, A326116(12) = 1232.
%C A308542 If this sequence counts product-closed sets, A326116 counts product-free sets.
%F A308542 For n > 0, a(n) = A326081(n)/2.
%e A308542 The a(6) = 28 sets:
%e A308542   {}  {2}  {2,4}  {2,3,6}  {2,3,4,6}  {2,3,4,5,6}
%e A308542       {3}  {2,5}  {2,4,5}  {2,3,5,6}
%e A308542       {4}  {2,6}  {2,4,6}  {2,4,5,6}
%e A308542       {5}  {3,4}  {2,5,6}  {3,4,5,6}
%e A308542       {6}  {3,5}  {3,4,5}
%e A308542            {3,6}  {3,4,6}
%e A308542            {4,5}  {3,5,6}
%e A308542            {4,6}  {4,5,6}
%e A308542            {5,6}
%t A308542 Table[Length[Select[Subsets[Range[2,n]],SubsetQ[#,Select[Times@@@Subsets[#,{2}],#<=n&]]&]],{n,0,10}]
%Y A308542 Cf. A007865, A051026, A103580, A196724, A326020, A326023, A326076, A326078, A326079, A326081, A326116, A326117.
%K A308542 nonn
%O A308542 1,2
%A A308542 _Gus Wiseman_, Jun 06 2019
%E A308542 Terms a(21) and beyond from _Andrew Howroyd_, Aug 24 2019