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A326492
Number of maximal subsets of {1..n} containing no quotients of pairs of distinct elements.
5
1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 7, 7, 10, 10, 16, 18, 31, 31, 47, 47, 52, 62, 104, 104, 130, 159, 283, 283, 323, 323, 554, 554, 616, 690, 1248, 1366, 1871, 1871, 3567, 3759, 5245, 5245, 8678, 8678, 9808, 12148, 23352, 23352, 27470, 31695, 45719, 47187, 54595, 54595, 95383, 108199
OFFSET
0,3
FORMULA
a(n) = A326496(n) + 1 for n > 1. - Andrew Howroyd, Aug 30 2019
EXAMPLE
The a(0) = 1 through a(9) = 5 subsets:
{} {1} {1} {1} {1} {1} {1} {1} {1} {1}
{2} {23} {23} {235} {235} {2357} {23578} {23578}
{34} {345} {256} {2567} {25678} {256789}
{3456} {34567} {345678} {345678}
{456789}
MATHEMATICA
fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]], Intersection[#, Divide@@@Select[Tuples[#, 2], UnsameQ@@#&&Divisible@@#&]]=={}&]]], {n, 0, 10}]
CROSSREFS
Subsets with quotients are A326023.
Subsets with quotients > 1 are A326079.
Subsets without quotients are A327591.
Maximal subsets without differences or quotients are A326491.
Maximal subsets without quotients (or products) are A326496.
Sequence in context: A181988 A194173 A028825 * A132924 A076890 A103358
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 09 2019
EXTENSIONS
Terms a(16) and beyond from Andrew Howroyd, Aug 30 2019
STATUS
approved