

A253258


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


5



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
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OFFSET

1,2


COMMENTS

This is a permutation of the natural numbers.
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



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.


KEYWORD



AUTHOR



EXTENSIONS



STATUS

approved



