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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.

%I A192298 #17 Oct 21 2024 09:01:40
%S A192298 1,1,2,3,2,4,6,6,10,14,13,26,34,24,48,72,60,120,168,168,264,396,312,
%T A192298 624,816,816,1632,2208
%N A192298 The number of sets of n positive integers strictly less than 2*n such that no integer in the set divides another.
%C A192298 Similar to A174094, but the maximum integer in each set must be strictly less than 2n here.
%e A192298 a(1) counts {1};
%e A192298 a(2) counts {2,3};
%e A192298 a(3) counts {2,3,5} and {3,4,5};
%e A192298 a(4) counts {2,3,5,7}, {3,4,5,7}, and {4,5,6,7};
%e A192298 a(5) counts {4,5,6,7,9} and {5,6,7,8,9}.
%p A192298 with(combstruct) ;
%p A192298 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:
%p A192298 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
%Y A192298 Cf. A174094.
%K A192298 nonn,more
%O A192298 1,3
%A A192298 _David Brown_, Jun 27 2011