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A075383

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

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, 49, 56, 32, 40, 64, 72, 80, 88, 96, 104, 27, 45, 63, 81, 90, 99, 108, 117, 126, 50, 60, 70, 100, 110, 120, 130, 140, 150, 160, 11, 22, 33, 44, 55, 66, 77, 121, 132, 143, 154, 84

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OFFSET

1,2

COMMENTS

Integer permutation with inverse A096780: a(A096780(n))=A096780(a(n))=n; A096781(n) = a(a(n)). - Reinhard Zumkeller, Jul 09 2004

Primes occur in natural order: a(A072205(n)) = A000040(n). - Reinhard Zumkeller, Jun 22 2009

n = greatest common divisor of row n. - Reinhard Zumkeller, Nov 30 2015

LINKS

R. Zumkeller, Table of n, a(n) for n = 1..10000 - Reinhard Zumkeller, Jun 22 2009

Index entries for sequences that are permutations of the natural numbers

EXAMPLE

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, 49, 56;

32, ...

MATHEMATICA

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 *)

PROG

(Haskell)

import Data.List ((\\))

a075383 n k = a075383_tabl !! (n-1) !! (k-1)

a075383_row n = a075383_tabl !! (n-1)

a075383_tabl = f 1 [1..] where

f x zs = ys : f (x + 1) (zs \\ ys) where

ys = take x $ filter ((== 0) . (`mod` x)) zs

a075383_list = concat a075383_tabl

-- Reinhard Zumkeller, Nov 30 2015

CROSSREFS

Cf. A075384, A075385, A075386, A075387, A075388, A075389, A075390.