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
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