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A308542
Number of subsets of {2..n} containing the product of any set of distinct elements whose product is <= n.
3
1, 2, 4, 8, 16, 28, 56, 100, 200, 364, 728, 1184, 2368, 4448, 8056, 15008, 30016, 52736, 105472, 183424, 339840, 663616, 1327232, 2217088, 4434176, 8744320, 16559168, 30034624, 60069248, 103402112, 206804224, 379941440, 730800064, 1454649248, 2659869664, 4786282208
OFFSET
1,2
COMMENTS
First differs from A326116 at a(12) = 1184, A326116(12) = 1232.
If this sequence counts product-closed sets, A326116 counts product-free sets.
FORMULA
For n > 0, a(n) = A326081(n)/2.
EXAMPLE
The a(6) = 28 sets:
{} {2} {2,4} {2,3,6} {2,3,4,6} {2,3,4,5,6}
{3} {2,5} {2,4,5} {2,3,5,6}
{4} {2,6} {2,4,6} {2,4,5,6}
{5} {3,4} {2,5,6} {3,4,5,6}
{6} {3,5} {3,4,5}
{3,6} {3,4,6}
{4,5} {3,5,6}
{4,6} {4,5,6}
{5,6}
MATHEMATICA
Table[Length[Select[Subsets[Range[2, n]], SubsetQ[#, Select[Times@@@Subsets[#, {2}], #<=n&]]&]], {n, 0, 10}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 06 2019
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Aug 24 2019
STATUS
approved