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A326497 Number of maximal sum-free and product-free subsets of {1..n}. 9
1, 1, 1, 1, 2, 3, 4, 6, 8, 9, 15, 21, 26, 38, 51, 69, 89, 119, 149, 197, 261, 356, 447, 601, 781, 1003, 1293, 1714, 2228, 2931, 3697, 4843, 6258, 8187, 10273, 13445, 16894, 21953, 27469, 35842, 45410, 58948, 73939, 95199, 120593, 154510, 192995, 247966, 312642 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
A set is sum-free and product-free if it contains no sum or product of two (not necessarily distinct) elements.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..68
Andrew Howroyd, PARI Program
EXAMPLE
The a(2) = 1 through a(10) = 15 subsets (A = 10):
{2} {23} {23} {23} {23} {237} {256} {267} {23A}
{34} {25} {256} {256} {258} {345} {345}
{345} {345} {267} {267} {357} {34A}
{456} {345} {345} {2378} {357}
{357} {357} {2569} {38A}
{4567} {2378} {2589} {2378}
{4567} {4567} {2569}
{5678} {4679} {2589}
{56789} {267A}
{269A}
{4567}
{4679}
{479A}
{56789}
{6789A}
MATHEMATICA
fasmax[y_]:=Complement[y, Union@@(Most[Subsets[#]]&/@y)];
Table[Length[fasmax[Select[Subsets[Range[n]], Intersection[#, Union[Plus@@@Tuples[#, 2], Times@@@Tuples[#, 2]]]=={}&]]], {n, 0, 10}]
PROG
(PARI) \\ See link for program file.
for(n=0, 37, print1(A326497(n), ", ")) \\ Andrew Howroyd, Aug 30 2019
CROSSREFS
Sum-free and product-free subsets are A326495.
Sum-free subsets are A007865.
Maximal sum-free subsets are A121269.
Product-free subsets are A326489.
Maximal product-free subsets are A326496.
Subsets with sums (and products) are A326083.
Sequence in context: A338349 A343377 A073667 * A325046 A160256 A151545
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 09 2019
EXTENSIONS
a(21)-a(40) from Andrew Howroyd, Aug 30 2019
a(41)-a(48) from Jinyuan Wang, Oct 11 2020
STATUS
approved

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Last modified February 24 07:07 EST 2024. Contains 370294 sequences. (Running on oeis4.)