A192298 The number of sets of n positive integers strictly less than 2*n 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

Author

David Brown, Jun 27 2011

Keywords

• nonn
• more

Comments

Similar to A174094, but the maximum integer in each set must be strictly less than 2n here.

Examples

			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}.
		

Crossrefs

Cf. A174094.

Programs

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