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A075383 Rearrangement of natural numbers so that next n numbers are each divisible by n.

%I A075383 #28 Apr 28 2017 12:02:25
%S A075383 1,2,4,3,6,9,8,12,16,20,5,10,15,25,30,18,24,36,42,48,54,7,14,21,28,35,
%T A075383 49,56,32,40,64,72,80,88,96,104,27,45,63,81,90,99,108,117,126,50,60,
%U A075383 70,100,110,120,130,140,150,160,11,22,33,44,55,66,77,121,132,143,154,84
%N A075383 Rearrangement of natural numbers so that next n numbers are each divisible by n.
%C A075383 Integer permutation with inverse A096780: a(A096780(n))=A096780(a(n))=n; A096781(n) = a(a(n)). - _Reinhard Zumkeller_, Jul 09 2004
%C A075383 Primes occur in natural order: a(A072205(n)) = A000040(n). - _Reinhard Zumkeller_, Jun 22 2009
%C A075383 n = greatest common divisor of row n. - _Reinhard Zumkeller_, Nov 30 2015
%H A075383 R. Zumkeller, <a href="/A075383/b075383.txt">Table of n, a(n) for n = 1..10000</a> - _Reinhard Zumkeller_, Jun 22 2009
%H A075383 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A075383    1;
%e A075383    2,  4;
%e A075383    3,  6,  9;
%e A075383    8, 12, 16, 20;
%e A075383    5, 10, 15, 25, 30;
%e A075383   18, 24, 36, 42, 48, 54;
%e A075383    7, 14, 21, 28, 35, 49, 56;
%e A075383   32, ...
%t A075383 row[1] = {1}; row[n_] := row[n] = (For[rows = Join[row /@ Range[n-1]]; ro = {}; k = n, Length[ro] < n, k = k+n, If[FreeQ[rows, k], AppendTo[ro, k]]]; ro); Array[row, 12] // Flatten (* _Jean-François Alcover_, Apr 28 2017 *)
%o A075383 (Haskell)
%o A075383 import Data.List ((\\))
%o A075383 a075383 n k = a075383_tabl !! (n-1) !! (k-1)
%o A075383 a075383_row n = a075383_tabl !! (n-1)
%o A075383 a075383_tabl = f 1 [1..] where
%o A075383    f x zs = ys : f (x + 1) (zs \\ ys) where
%o A075383             ys = take x $ filter ((== 0) . (`mod` x)) zs
%o A075383 a075383_list = concat a075383_tabl
%o A075383 -- _Reinhard Zumkeller_, Nov 30 2015
%Y A075383 Cf. A075384, A075385, A075386, A075387, A075388, A075389, A075390.
%Y A075383 Cf. A000040, A072205, A096780, A096781, A263896 (central terms).
%K A075383 nonn,tabl,look,easy
%O A075383 1,2
%A A075383 _Amarnath Murthy_, Sep 22 2002
%E A075383 More terms from _Sascha Kurz_, Jan 28 2003