A192298 The number of sets of n positive integers strictly less than 2n such that no integer in the set divides another.

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.

Links

Table of n, a(n) for n=1..28.

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

Adjacent sequences: A192295 A192296 A192297 * A192299 A192300 A192301

Keyword

nonn,more

Author

David Brown, Jun 27 2011

Status

approved