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 A326081 Number of subsets of {1..n} containing the product of any set of distinct elements whose product is <= n. 9
 1, 2, 4, 8, 16, 32, 56, 112, 200, 400, 728, 1456, 2368, 4736, 8896, 16112, 30016, 60032, 105472, 210944, 366848, 679680, 1327232, 2654464, 4434176, 8868352, 17488640, 33118336, 60069248, 120138496, 206804224, 413608448, 759882880, 1461600128, 2909298496, 5319739328 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For n > 0, this sequence divided by 2 first differs from A326116 at a(12)/2 = 1184, A326116(12) = 1232. If A326117 counts product-free sets, this sequence counts product-closed sets. The non-strict case is A326076. LINKS FORMULA For n > 0, a(n) = 2 * A308542(n). EXAMPLE The a(6) = 56 subsets:   {}  {1}  {1,2}  {1,2,4}  {1,2,3,6}  {1,2,3,4,6}  {1,2,3,4,5,6}       {2}  {1,3}  {1,2,5}  {1,2,4,5}  {1,2,3,5,6}       {3}  {1,4}  {1,2,6}  {1,2,4,6}  {1,2,4,5,6}       {4}  {1,5}  {1,3,4}  {1,2,5,6}  {1,3,4,5,6}       {5}  {1,6}  {1,3,5}  {1,3,4,5}  {2,3,4,5,6}       {6}  {2,4}  {1,3,6}  {1,3,4,6}            {2,5}  {1,4,5}  {1,3,5,6}            {2,6}  {1,4,6}  {1,4,5,6}            {3,4}  {1,5,6}  {2,3,4,6}            {3,5}  {2,3,6}  {2,3,5,6}            {3,6}  {2,4,5}  {2,4,5,6}            {4,5}  {2,4,6}  {3,4,5,6}            {4,6}  {2,5,6}            {5,6}  {3,4,5}                   {3,4,6}                   {3,5,6}                   {4,5,6} MATHEMATICA Table[Length[Select[Subsets[Range[n]], SubsetQ[#, Select[Times@@@Subsets[#, {2}], #<=n&]]&]], {n, 0, 10}] CROSSREFS Cf. A007865, A051026, A103580, A196724, A308542, A326020, A326023, A326076, A326078, A326079. Sequence in context: A329824 A229614 A230216 * A245392 A115909 A254940 Adjacent sequences:  A326078 A326079 A326080 * A326082 A326083 A326084 KEYWORD nonn AUTHOR Gus Wiseman, Jun 05 2019 EXTENSIONS Terms a(21) and beyond from Andrew Howroyd, Aug 24 2019 STATUS approved

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Last modified June 6 04:04 EDT 2020. Contains 334858 sequences. (Running on oeis4.)