A253258 Square array read by antidiagonals, j>=1, k>=1: T(j,k) is the j-th number n such that the symmetric representation of sigma(n) has at least a part with maximum width k.

1, 2, 6, 3, 12, 60, 4, 15, 72, 120, 5, 18, 84, 180, 360, 7, 20, 90, 240, 420, 840, 8, 24, 126, 252, 720, 1080, 3360, 9, 28, 140, 336, 1008, 1260, 3600, 2520, 10, 30, 144, 378, 1200, 1440, 3780, 5544, 5040, 11, 35, 168, 432, 1320, 1680, 3960, 6300, 7560, 10080, 13, 36, 198, 480, 1512, 1800, 4200, 6720, 9240, 12600, 15120

Offset

1,2

Comments

This is a permutation of the natural numbers.

Row 1 gives A250070.

For more information about the widths of the symmetric representation of sigma see A249351 and A250068.

The next term: 120 < T(2,4) < 360.

Links

Table of n, a(n) for n=1..66.

Index entries for sequences that are permutations of the natural numbers

Example

The corner of the square array T(j,k) begins:
1,  6, 60, 120, 360, ...
2, 12, 72, ...
3, 15, 84, ...
4, 18, ...
5, 20, ...
7, ...
...
For j = 1 and k = 2; T(1,2) is the first number n such that the symmetric representation of sigma(n) has a part with maximum width 2 as shown below:
.
.      Dyck paths            Cells              Widths
.     _ _ _ _             _ _ _ _
.     _ _ _  |_          |_|_|_|_|_          / / / /
.          |   |_              |_|_|_              / /
.          |_ _  |             |_|_|_|             / / /
.              | |                 |_|                 /
.              | |                 |_|                 /
.              | |                 |_|                 /
.
The widths of the symmetric representation of sigma(6) = 12 are [1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1], also the 6th row of triangle A249351.

Crossrefs

Cf. A000203, A196020, A235791, A236104, A237048, A237270, A237271, A237591, A237593, A245092, A249351, A250068, A250070, A250071.

Sequence in context: A054619 A054618 A120859 * A098810 A360006 A081469

Adjacent sequences: A253255 A253256 A253257 * A253259 A253260 A253261

Keyword

nonn,tabl

Author

Omar E. Pol, Jul 08 2015

Extensions

More terms from Charlie Neder, Jan 11 2019

Status

approved