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A192298
The number of sets of n positive integers strictly less than 2*n such that no integer in the set divides another.
2
1, 1, 2, 3, 2, 4, 6, 6, 10, 14, 13, 26, 34, 24, 48, 72, 60, 120, 168, 168, 264, 396, 312, 624, 816, 816, 1632, 2208
OFFSET
1,3
COMMENTS
Similar to A174094, but the maximum integer in each set must be strictly less than 2n here.
EXAMPLE
a(1) counts {1};
a(2) counts {2,3};
a(3) counts {2,3,5} and {3,4,5};
a(4) counts {2,3,5,7}, {3,4,5,7}, and {4,5,6,7};
a(5) counts {4,5,6,7,9} and {5,6,7,8,9}.
MAPLE
with(combstruct) ;
A192298nodiv := proc(s) sl := sort(convert(s, list)) ; for i from 1 to nops(sl)-1 do for j from i+1 to nops(sl) do if op(j, sl) mod op(i, sl) = 0 then return false; end if; end do: end do:true ; end proc:
A192298 := proc(n) a := 0 ; it := iterstructs(Subset({seq(i, i=1..2*n-1)}, size=n)) : while not finished(it) do s := nextstruct(it) ; if nops(s) = n then if A192298nodiv(s) then a := a+1 ; end if; end if; end do: a ; end proc: # R. J. Mathar, Jul 12 2011
CROSSREFS
Cf. A174094.
Sequence in context: A244306 A345199 A079159 * A341098 A353330 A254967
KEYWORD
nonn,more
AUTHOR
David Brown, Jun 27 2011
STATUS
approved