A075384 -id:A075384 - cp's OEIS frontend

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

Offset: 1

Amarnath Murthy, Sep 22 2002

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

			   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, ...

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

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

Cf. A000040, A072205, A096780, A096781, A263896 (central terms).

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

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 *)

More terms from Sascha Kurz, Jan 28 2003

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

Amarnath Murthy, Sep 22 2002

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Cf. A075383, A075384, A075385, A075387, A075390.

a075386 = sum . a075383_row  -- Reinhard Zumkeller, Nov 29 2015

More terms from David Wasserman, Jan 17 2005

A075385 Final term of n-th group in A075383.

Original entry on oeis.org

1, 4, 9, 20, 30, 54, 56, 104, 126, 160, 154, 264, 234, 364, 390, 480, 374, 630, 475, 780, 819, 946, 713, 1200, 1100, 1326, 1350, 1596, 1160, 1950, 1333, 2144, 2046, 2312, 2380, 2844, 1961, 3002, 3081, 3600, 2378, 3948, 2666, 4136, 4275, 4370, 3149, 5280

Offset: 1

Amarnath Murthy, Sep 22 2002

nonn

Cf. A075383, A075384, A075386, A075387, A075389.

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

Amarnath Murthy, Sep 22 2002

nonn

Cf. A075383, A075384, A075385, A075386, A075391.

a075387 = product . a075383_row  -- Reinhard Zumkeller, Nov 29 2015

More terms from David Wasserman, Jan 17 2005

A095164 Index of the first occurrence of n in A095163.

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

Offset: 1

Amarnath Murthy, Jun 01 2004

nonn

Is this the same as A075384? - R. J. Mathar, Oct 28 2008

Cf. A095161, A095162, A095163, A095165.

A095163 := proc(nmax) local a,dvs,d,n; a := [1,2,3] ; for n from 4 to nmax do dvs := sort(convert(numtheory[divisors](n),list)) ; for d in dvs do if ListTools[Occurrences](d,a) < d then a := [op(a),d] ; break; fi; od: od: a ; end: A095164 := proc(n,a095163) local i ; for i from 1 to nops(a095163) do if op(i,a095163) = n then RETURN(i) ; fi; od: RETURN(-1) ; end: a095163 := A095163(3700) ; for n from 1 do a095 := A095164(n,a095163) ; if a095 < 0 then break; else printf("%d,",a095) ; fi; od: # R. J. Mathar, Oct 28 2008

More terms from Nadia Heninger, Jul 07 2005

More terms from R. J. Mathar, Oct 28 2008

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

Amarnath Murthy, Sep 22 2002

nonn

A075384(n)/n

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Cf. A075383, A075384, A075385, A075386.

a075388 n = a075384 n `div` n -- Reinhard Zumkeller, Nov 29 2015

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

Amarnath Murthy, Sep 22 2002

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Cf. A075383, A075384, A075385, A075386.

a075390 n = a075386 n `div` n -- Reinhard Zumkeller, Nov 29 2015

A075386(n)/n

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

Amarnath Murthy, Sep 22 2002

nonn

Cf. A075383, A075384, A075385, A075386.

A075385(n)/n

More terms from Sascha Kurz, Jan 28 2003

A096776 n / Max{a(k): 1<=k

Original entry on oeis.org

1, 2, 3, 2, 5, 2, 7, 4, 3, 2, 11, 3, 13, 2, 3, 4, 17, 6, 19, 4, 3, 2, 23, 4, 5, 2, 9, 4, 29, 5, 31, 8, 3, 2, 5, 4, 37, 2, 3, 5, 41, 6, 43, 4, 5, 2, 47, 6, 7, 10, 3, 4, 53, 6, 5, 7, 3, 2, 59, 6, 61, 2, 7, 8, 5, 6, 67, 4, 3, 7, 71, 8, 73, 2, 15, 4, 7, 6, 79, 8, 9, 2, 83, 12, 5, 2, 3, 8, 89, 6, 7

Offset: 1

Reinhard Zumkeller, Jul 09 2004

nonn

a(n)=n iff n=1 or n is prime;

Removed comment on relation with A075384. - R. J. Mathar, Oct 31 2008

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

Amarnath Murthy, Sep 22 2002

nonn

Cf. A075383, A075384, A075385, A075386, A075387.

A075387(n)/(n^n)

More terms from David Wasserman, Jan 17 2005

cp's OEIS Frontend

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

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

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A075385 Final term of n-th group in A075383.

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

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A095164 Index of the first occurrence of n in A095163.

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

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A075390 Average of n-th group in A075383.

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

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A096776 n / Max{a(k): 1<=k

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

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