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.

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, 27, 32, 30, 14, 96, 17, 162, 42, 60, 40, 144, 19, 33, 90, 216, 22, 120, 23, 84, 64, 39, 25, 324, 35, 168, 50, 270, 26, 192, 56, 180, 44, 126, 29, 288, 31, 51, 80, 486

Offset: 1

Author

Alois P. Heinz, Feb 12 2013

Keywords

• nonn

Comments

Permutation of the natural numbers A000027 with inverse permutation A222209.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000027, A211384, A222209.

Cf. A027751.

Programs

Haskell

import Data.List (delete)
a222208 n = a222208_list !! (n-1)
a222208_list = 1 : 3 : f 3 (2 : [4 ..]) where
   f u vs = g vs where
     g (w:ws) = if all (== 0) $ map ((mod w) . a222208) $ a027751_row u
                   then w : f (u + 1) (delete w vs) else g ws
-- Reinhard Zumkeller, Feb 13 2013

Maple

b:= proc(n) false end:
a:= proc(n) option remember; local h, i;
      if n<3 then h:= 2*n-1 else a(n-1); h:= ilcm(map(a,
         numtheory[divisors](n) minus {1, n})[]) fi;
      for i while b(i*h) do od;
      b(i*h):= true; i*h
    end:
seq(a(n), n=1..100);

Mathematica

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]]]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 22 2017 *)