A348357 Square array T(n, k), n, k > 0, read by antidiagonal upwards; the k-th column contains, in ascending order, the integers m such that A348331(m) = k.

1, 2, 4, 3, 5, 7, 6, 9, 8, 10, 12, 18, 15, 11, 13, 24, 36, 30, 21, 14, 16, 48, 72, 60, 42, 27, 17, 19, 96, 144, 120, 84, 54, 33, 20, 22, 192, 288, 240, 168, 108, 66, 39, 23, 25, 384, 576, 480, 336, 216, 132, 78, 45, 26, 28, 768, 1152, 960, 672, 432, 264, 156, 90, 51, 29, 31

Offset: 1

Author

Rémy Sigrist, Oct 14 2021

Keywords

• nonn
• tabl

Comments

When interpreted as a flat array, we have a permutation of the positive integers.

Examples

			Array T(n, k) begins:
  n\k|    1     2     3     4     5     6     7     8     9    10
  ---+-----------------------------------------------------------
    1|    1     4     7    10    13    16    19    22    25    28
    2|    2     5     8    11    14    17    20    23    26    29
    3|    3     9    15    21    27    33    39    45    51    57
    4|    6    18    30    42    54    66    78    90   102   114
    5|   12    36    60    84   108   132   156   180   204   228
    6|   24    72   120   168   216   264   312   360   408   456
    7|   48   144   240   336   432   528   624   720   816   912
    8|   96   288   480   672   864  1056  1248  1440  1632  1824
    9|  192   576   960  1344  1728  2112  2496  2880  3264  3648
   10|  384  1152  1920  2688  3456  4224  4992  5760  6528  7296
		

Links

• Rémy Sigrist, PARI program for A348357
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A098011, A348331, A348356.

Programs

PARI

See Links section.

Formula

Sum_{i = 1..n-1} T(i, k) <= T(n, k).

T(n, 1) = A098011(n+1).