A338918 -id:A338918 - cp's OEIS frontend

A338919 Square array of distinct positive integers T(n, k), n > 0, k > 0, read by antidiagonals upwards, filled the greedy way such that for any n > 0 and k > 0, T(n, k) is divisible by n and by k.

1, 2, 4, 3, 6, 9, 8, 12, 18, 16, 5, 20, 15, 24, 10, 30, 40, 36, 48, 50, 42, 7, 54, 45, 28, 60, 66, 14, 32, 56, 72, 80, 100, 78, 70, 64, 27, 88, 21, 84, 25, 96, 63, 104, 81, 90, 108, 120, 112, 150, 180, 140, 144, 126, 110, 11, 130, 99, 128, 35, 102, 105, 136, 117, 160, 22

Offset: 1

Rémy Sigrist, Nov 15 2020

All integers appear in this sequence.

			Array T(n, k) begins:
  n\k|   1    2    3    4    5    6    7    8    9   10
  ---+-------------------------------------------------
    1|   1    4    9   16   10   42   14   64   81  110
    2|   2    6   18   24   50   66   70  104  126  160
    3|   3   12   15   48   60   78   63  144  117  270
    4|   8   20   36   28  100   96  140  136  288  260
    5|   5   40   45   80   25  180  105  240  225  190
    6|  30   54   72   84  150  102  252  312  198  360
    7|   7   56   21  112   35  168   49  280  315  490
    8|  32   88  120  128  200  264  224  152  504  400
    9|  27  108   99  216  135  162  189  432  153  720
   10|  90  130  210  220  170  330  350  320  630  230

Rémy Sigrist, Table of n, a(n) for n = 1..5050
Rémy Sigrist, PARI program for A338919
Index entries for sequences that are permutations of the natural numbers

See A338872 and A338918 for similar sequences.

PARI
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See Links section.
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T(p, 1) = p for any prime number p.

A338872 Square array of distinct positive integers T(n, k), n > 0, k > 0, read by antidiagonals upwards, filled the greedy way such that for any n > 0 and k > 0, Sum_{ i = 1..n, j = 1..k } T(i, j) is divisible by n * k.

Original entry on oeis.org

1, 3, 5, 2, 7, 6, 10, 12, 8, 4, 9, 16, 19, 14, 24, 11, 15, 31, 27, 18, 20, 13, 17, 21, 43, 30, 22, 38, 23, 33, 41, 47, 40, 48, 26, 46, 36, 63, 35, 39, 88, 70, 44, 62, 45, 32, 66, 55, 71, 52, 60, 28, 42, 29, 51, 25, 86, 90, 67, 98, 56, 54, 34, 73, 91, 57

Offset: 1

Rémy Sigrist, Nov 13 2020

This sequence is a 2-dimensional variant of A019444.

			Array T(n, k) begins:
  n\k|   1   2   3    4    5    6    7    8    9   10
  ---+-----------------------------------------------
    1|   1   5   6    4   24   20   38   46   45   51
    2|   3   7   8   14   18   22   26   62   29   91
    3|   2  12  19   27   30   48   44   42   73   53
    4|  10  16  31   43   40   70   28   34   61   37
    5|   9  15  21   47   88   60   54  106   77  133
    6|  11  17  41   39   52   56   50  118  129  157
    7|  13  33  35   71   98  116  173  117  181  213
    8|  23  63  55   67   82  136  155  187  141  161
    9|  36  66  90   84   99  111  179  143  146  256
   10|  32  86  74  124  109  121  203  235   78  188

Rémy Sigrist, Table of n, a(n) for n = 1..5050
Rémy Sigrist, PARI program for A338872

See A338918 and A338919 for similar sequences.

Cf. A019444.

PARI
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See Links section.
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cp's OEIS Frontend

A338919 Square array of distinct positive integers T(n, k), n > 0, k > 0, read by antidiagonals upwards, filled the greedy way such that for any n > 0 and k > 0, T(n, k) is divisible by n and by k.

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