OFFSET
0,3
COMMENTS
These sets are closed under taking the quotient of two distinct divisible terms.
EXAMPLE
The a(6) = 24 subsets:
{} {2} {2,3} {2,3,4} {2,3,4,5} {2,3,4,5,6}
{3} {2,4} {2,3,5} {2,3,4,6}
{4} {2,5} {2,3,6} {2,3,5,6}
{5} {3,4} {2,4,5}
{6} {3,5} {3,4,5}
{4,5} {4,5,6}
{4,6}
{5,6}
MATHEMATICA
Table[Length[Select[Subsets[Range[2, n]], SubsetQ[#, Divide@@@Select[Tuples[#, 2], UnsameQ@@#&&Divisible@@#&]]&]], {n, 0, 10}]
PROG
(PARI)
a(n)={
my(lim=vector(n, k, sqrtint(k)));
my(accept(b, k)=for(i=2, lim[k], if(k%i ==0 && bittest(b, i) != bittest(b, k/i), return(0))); 1);
my(recurse(k, b)=
my(m=1);
for(j=max(2*k, n\2+1), min(2*k+1, n), if(accept(b, j), m*=2));
k++;
m*if(k > n\2, 1, (self()(k, b) + if(accept(b, k), self()(k, b + (1<<k)))))
);
recurse(1, 0);
} \\ Andrew Howroyd, Aug 30 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 05 2019
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Aug 30 2019
STATUS
approved