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A326078
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Number of subsets of {2..n} containing all of their integer quotients > 1.
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8
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1, 1, 2, 4, 8, 16, 24, 48, 72, 144, 216, 432, 552, 1104, 1656, 2592, 3936, 7872, 10056, 20112, 26688, 42320, 63480, 126960, 154800, 309600, 464400, 737568, 992160, 1984320, 2450880, 4901760, 6292800, 10197312, 15295968, 26241696, 32947488, 65894976, 98842464, 161587872, 205842528
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OFFSET
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0,3
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COMMENTS
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These sets are closed under taking the quotient of two distinct divisible terms.
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LINKS
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FORMULA
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EXAMPLE
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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}
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MATHEMATICA
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Table[Length[Select[Subsets[Range[2, n]], SubsetQ[#, Divide@@@Select[Tuples[#, 2], UnsameQ@@#&&Divisible@@#&]]&]], {n, 0, 10}]
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PROG
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(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);
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CROSSREFS
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Cf. A007865, A051026, A054519, A067992, A103580, A325860, A325994, A326023, A326076, A326079, A326081.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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