login
A325710
Number of maximal subsets of {1..n} containing no products of distinct elements.
6
1, 1, 2, 2, 2, 2, 4, 4, 6, 6, 10, 10, 14, 14, 24, 28, 32, 32, 62, 62, 92, 102, 184, 184, 254, 254, 474, 506, 686, 686, 1172, 1172, 1792, 1906, 3568, 3794, 5326, 5326, 10282, 10618, 14822, 14822, 25564, 25564, 35304, 39432, 76888, 76888, 100574, 100574, 197870, 201622, 282014
OFFSET
0,3
EXAMPLE
The a(1) = 1 through a(9) = 6 maximal subsets:
{1} {1} {1} {1} {1} {1} {1} {1} {1}
{2} {23} {234} {2345} {2345} {23457} {23457} {234579}
{2456} {24567} {23578} {235789}
{3456} {34567} {24567} {245679}
{25678} {256789}
{345678} {3456789}
MATHEMATICA
fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]], Intersection[#, Times@@@Subsets[#, {2, n}]]=={}&]]], {n, 0, 10}]
PROG
(PARI) \\ See link for program file.
for(n=0, 30, print1(A325710(n), ", ")) \\ Andrew Howroyd, Aug 29 2019
CROSSREFS
Subsets without products of distinct elements are A326117.
Maximal product-free subsets are A326496.
Subsets with products are A326076.
Maximal subsets without sums of distinct elements are A326498.
Maximal subsets without quotients are A326492.
Maximal subsets without sums or products of distinct elements are A326025.
Sequence in context: A347325 A324762 A104976 * A214927 A326115 A355746
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 09 2019
EXTENSIONS
Terms a(16) and beyond from Andrew Howroyd, Aug 29 2019
STATUS
approved