cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

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

Original entry on oeis.org

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
Offset: 1

Views

Author

Amarnath Murthy, Sep 22 2002

Keywords

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

Examples

			   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, ...
		

Crossrefs

Programs

  • 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
  • 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 *)

Extensions

More terms from Sascha Kurz, Jan 28 2003

A075384 Initial term of n-th group in A075383.

Original entry on oeis.org

1, 2, 3, 8, 5, 18, 7, 32, 27, 50, 11, 84, 13, 98, 75, 128, 17, 162, 19, 200, 147, 242, 23, 312, 125, 338, 243, 392, 29, 510, 31, 512, 363, 578, 245, 684, 37, 722, 507, 920, 41, 882, 43, 968, 765, 1058, 47, 1392, 343, 1250, 867, 1352, 53, 1458, 605, 1624, 1083, 1682, 59, 2220, 61, 1922, 1449, 2368, 845
Offset: 1

Views

Author

Amarnath Murthy, Sep 22 2002

Keywords

Crossrefs

Programs

  • Haskell
    a075384 = head . a075383_row  -- Reinhard Zumkeller, Nov 29 2015
  • Maple
    A075383 := proc(nmax) local a,n,ct,k; a := [1,2,4] ; for n from 3 do ct := 0 ; for k from 1 do if (k*n) in a then ; else a := [op(a),k*n] ; ct := ct+1 ; if ct >= n then break ; fi ; fi; od: if nops(a) > nmax then RETURN(a) ; fi; od: end: A075384 := proc(n,a075383) local i,k ; i := 1 ; for k from 1 to n-1 do i := i+k ; if i > nops(a075383) then RETURN(-1) ; fi; od: RETURN(op(i,a075383)) ; end: a075383 := A075383(4000) : for n from 1 to 70 do a084 := A075384(n,a075383) ; if a084 < 0 then break; else printf("%d,",a084) ; fi; od:
  • Mathematica
    row[n_] := row[n] = If[n == 1, {1}, rows = Join[row /@ Range[n-1]]; ro = {}; For[k = n, Length[ro] < n, k = k + n, If[FreeQ[rows, k], AppendTo[ro, k]]]; ro]; a[n_] := row[n][[1]]; Array[a, 65] (* Jean-François Alcover, Jan 27 2018 *)

Extensions

More terms from Reinhard Zumkeller, Jul 09 2004
Removed claim on relation to A096776. Corrected from a(20) on by R. J. Mathar, Oct 31 2008

A075386 Sum of terms of n-th group in A075383.

Original entry on oeis.org

1, 6, 18, 56, 85, 222, 210, 576, 756, 1090, 858, 2328, 1573, 3598, 3930, 5488, 3111, 8154, 4427, 11060, 11676, 15004, 8073, 21336, 18125, 24726, 24516, 32060, 16530, 43410, 20243, 48576, 46101, 56780, 55685, 75780, 36186, 83106, 82524, 109480
Offset: 1

Views

Author

Amarnath Murthy, Sep 22 2002

Keywords

Crossrefs

Programs

Extensions

More terms from David Wasserman, Jan 17 2005

A075387 Product of terms of n-th group in A075383.

Original entry on oeis.org

1, 8, 162, 30720, 562500, 1693052928, 5534208960, 414571718246400, 87954833872105200, 121080960000000000000, 34545810976783666560, 1757453597218363858432819200, 20403194639791728130329600
Offset: 1

Views

Author

Amarnath Murthy, Sep 22 2002

Keywords

Crossrefs

Programs

Extensions

More terms from David Wasserman, Jan 17 2005

A075388 (1/n) times initial term of n-th group in A075383.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 7, 1, 7, 5, 8, 1, 9, 1, 10, 7, 11, 1, 13, 5, 13, 9, 14, 1, 17, 1, 16, 11, 17, 7, 19, 1, 19, 13, 23, 1, 21, 1, 22, 17, 23, 1, 29, 7, 25, 17, 26, 1, 27, 11, 29, 19, 29, 1, 37, 1, 31, 23, 37, 13, 33, 1, 37, 23, 37, 1, 41, 1, 37, 25, 41, 11, 41, 1, 47, 27, 41, 1, 53
Offset: 1

Views

Author

Amarnath Murthy, Sep 22 2002

Keywords

Comments

A075384(n)/n

Crossrefs

Programs

Extensions

More terms from David Wasserman, Jan 17 2005

A075390 Average of n-th group in A075383.

Original entry on oeis.org

1, 3, 6, 14, 17, 37, 30, 72, 84, 109, 78, 194, 121, 257, 262, 343, 183, 453, 233, 553, 556, 682, 351, 889, 725, 951, 908, 1145, 570, 1447, 653, 1518, 1397, 1670, 1591, 2105, 978, 2187, 2116, 2737, 1174, 2908, 1333, 2962, 2926, 3071, 1558, 4020, 2887, 3997, 3517
Offset: 1

Views

Author

Amarnath Murthy, Sep 22 2002

Keywords

Crossrefs

Programs

Formula

A075386(n)/n

Extensions

More terms from David Wasserman, Jan 17 2005

A075389 (1/n) times final term of n-th group in A075383.

Original entry on oeis.org

1, 2, 3, 5, 6, 9, 8, 13, 14, 16, 14, 22, 18, 26, 26, 30, 22, 35, 25, 39, 39, 43, 31, 50, 44, 51, 50, 57, 40, 65, 43, 67, 62, 68, 68, 79, 53, 79, 79, 90, 58, 94, 62, 94, 95, 95, 67, 110, 91, 109, 102, 113, 76, 122, 110, 126, 115, 123, 85, 144, 89, 132, 138, 144, 134, 151, 98
Offset: 1

Views

Author

Amarnath Murthy, Sep 22 2002

Keywords

Crossrefs

Formula

A075385(n)/n

Extensions

More terms from Sascha Kurz, Jan 28 2003

A075391 Product/n^n of n-th group in A075383.

Original entry on oeis.org

1, 2, 6, 120, 180, 36288, 6720, 24710400, 227026800, 12108096000, 121080960, 197110116403200, 67365043200, 201490341212160000, 1001829765736800000, 850009620666286080000, 2144384782848000, 5991810785878910952960000
Offset: 1

Views

Author

Amarnath Murthy, Sep 22 2002

Keywords

Crossrefs

Formula

A075387(n)/(n^n)

Extensions

More terms from David Wasserman, Jan 17 2005
Showing 1-8 of 8 results.