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A222208 a(1) = 1, a(2) = 3; for n>2, a(n) = smallest number not in {a(1), ..., a(n-1)} such that a(n) is divisible by a(d) for all divisors d of n.

%I A222208 #20 Jan 22 2017 13:32:48
%S A222208 1,3,2,6,4,12,5,18,8,24,7,36,9,15,16,54,10,48,11,72,20,21,13,108,28,
%T A222208 27,32,30,14,96,17,162,42,60,40,144,19,33,90,216,22,120,23,84,64,39,
%U A222208 25,324,35,168,50,270,26,192,56,180,44,126,29,288,31,51,80,486
%N A222208 a(1) = 1, a(2) = 3; for n>2, a(n) = smallest number not in {a(1), ..., a(n-1)} such that a(n) is divisible by a(d) for all divisors d of n.
%C A222208 Permutation of the natural numbers A000027 with inverse permutation A222209.
%H A222208 Alois P. Heinz, <a href="/A222208/b222208.txt">Table of n, a(n) for n = 1..10000</a>
%H A222208 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%p A222208 b:= proc(n) false end:
%p A222208 a:= proc(n) option remember; local h, i;
%p A222208       if n<3 then h:= 2*n-1 else a(n-1); h:= ilcm(map(a,
%p A222208          numtheory[divisors](n) minus {1, n})[]) fi;
%p A222208       for i while b(i*h) do od;
%p A222208       b(i*h):= true; i*h
%p A222208     end:
%p A222208 seq(a(n), n=1..100);
%t A222208 a[1] = 1; a[2] = 3; a[n_] := a[n] = Module[{d, s, c, k}, d = Divisors[n] ~Complement~ {1, n}; For[s = Sort[Array[a, n-1]]; c = Complement[ Range[ Last[s]], s]; k = If[c == {}, Last[s]+1, First[c]], True, k++, If[FreeQ[s, k], If[AllTrue[d, Divisible[k, a[#]]&], Return[k]]]]];
%t A222208 Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Jan 22 2017 *)
%o A222208 (Haskell)
%o A222208 import Data.List (delete)
%o A222208 a222208 n = a222208_list !! (n-1)
%o A222208 a222208_list = 1 : 3 : f 3 (2 : [4 ..]) where
%o A222208    f u vs = g vs where
%o A222208      g (w:ws) = if all (== 0) $ map ((mod w) . a222208) $ a027751_row u
%o A222208                    then w : f (u + 1) (delete w vs) else g ws
%o A222208 -- _Reinhard Zumkeller_, Feb 13 2013
%Y A222208 Cf. A000027, A211384, A222209.
%Y A222208 Cf. A027751.
%K A222208 nonn
%O A222208 1,2
%A A222208 _Alois P. Heinz_, Feb 12 2013