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A326490
Number of subsets of {1..n} containing no differences or quotients of pairs of distinct elements.
6
1, 2, 3, 5, 7, 12, 18, 31, 46, 72, 102, 172, 259, 428, 607, 989, 1329, 2142, 3117, 4953, 6956, 11032, 15321, 23979, 33380, 48699, 66849, 104853, 144712, 220758, 304133, 461580, 636556, 973843, 1316513, 1958828, 2585433, 3882843, 5237093, 7884277, 10555739, 15729293
OFFSET
0,2
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..90
FORMULA
For n > 0, a(n) = A326495(n) + 1.
EXAMPLE
The a(0) = 1 through a(6) = 18 subsets:
{} {} {} {} {} {} {}
{1} {1} {1} {1} {1} {1}
{2} {2} {2} {2} {2}
{3} {3} {3} {3}
{2,3} {4} {4} {4}
{2,3} {5} {5}
{3,4} {2,3} {6}
{2,5} {2,3}
{3,4} {2,5}
{3,5} {2,6}
{4,5} {3,4}
{3,4,5} {3,5}
{4,5}
{4,6}
{5,6}
{2,5,6}
{3,4,5}
{4,5,6}
MATHEMATICA
Table[Length[Select[Subsets[Range[n]], Intersection[#, Union[Divide@@@Reverse/@Subsets[#, {2}], Subtract@@@Reverse/@Subsets[#, {2}]]]=={}&]], {n, 0, 10}]
PROG
(PARI)
a(n)={
my(recurse(k, b)=
if(k > n, 1,
my(t = self()(k + 1, b));
for(i=1, k\2, if(bittest(b, i) && (bittest(b, k-i) || (!(k%i) && bittest(b, k/i))), return(t)));
t += self()(k + 1, b + (1<<k));
t);
);
if(n, recurse(2, 0)) + 1;
} \\ Andrew Howroyd, Aug 25 2019
CROSSREFS
Subsets without difference are A007865.
Maximal subsets without differences or quotients are A326491.
Subsets without quotients are A327591.
Subsets with differences and quotients are A326494.
Sequence in context: A169986 A218021 A137713 * A191385 A374746 A345669
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 09 2019
EXTENSIONS
a(19)-a(41) from Andrew Howroyd, Aug 25 2019
STATUS
approved