A348389 Irregular triangle read by rows: row n gives for n >= 2 a concatenation of the finite sequences of the multiples of k, larger than k and not exceeding n, for k = 1, 2, ..., floor(n/2).

2, 2, 3, 2, 3, 4, 4, 2, 3, 4, 5, 4, 2, 3, 4, 5, 6, 4, 6, 6, 2, 3, 4, 5, 6, 7, 4, 6, 6, 2, 3, 4, 5, 6, 7, 8, 4, 6, 8, 6, 8, 2, 3, 4, 5, 6, 7, 8, 9, 4, 6, 8, 6, 9, 8, 2, 3, 4, 5, 6, 7, 8, 9, 10, 4, 6, 8, 10, 6, 9, 8, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 4, 6, 8, 10, 6, 9, 8, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 4, 6, 8, 10, 12, 6, 9, 12, 8, 12, 10, 12

Offset

2,1

Comments

The length of row n is A002541(n).

The sum of row n is A348392(n).

The lengths of the sublists for these multiples of k in row n are given by T(n, k) = A348388(n, k), for n >= 2 and k = 1, 2, ..., floor(n/2).

Links

Table of n, a(n) for n=2..114.

Formula

The entries a(n, m) of row n, for n > = 2 and m = 1, 2, ..., A002541(n), are given by the concatenation of the sequences k*(2, 3, ..., t(n,k)) for k = 1, 2, ..., floor(n/2), with t(n, k) = floor((n-k)/k) + 1.

Example

The irregular triangle a(n, m) begins: (the k-sublists are separated by a vertical bar)
n\m   1 2 3 4 5 6 7 8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ...
-------------------------------------------------------------------------
2:    2
3:    2 3
4:    2 3 4|4
5:    2 3 4 5|4
6:    2 3 4 5 6|4 6|6
7:    2 3 4 5 6 7|4 6| 6
8:    2 3 4 5 6 7 8|4  6  8| 6| 8
9:    2 3 4 5 6 7 8 9| 4  6  8| 6  9| 8
10:   2 3 4 5 6 7 8 9 10| 4  6  8 10| 6  9| 8|10
11:   2 3 4 5 6 7 8 9 10 11| 4  6  8 10| 6  9| 8|10
12:   2 3 4 5 6 7 8 9 10 11 12| 4  6  8 10 12| 6  9 12| 8 12|10|12
13:   2 3 4 5 6 7 8 9 10 11 12 13| 4  6  8 10 12| 6  9 12| 8 12|10|12
...

Mathematica

nrows=10; Table[Flatten[Table[Range[2k, n, k], {k, Floor[n/2]}]], {n, 2, nrows+1}] (* Paolo Xausa, Nov 23 2021 *)

Crossrefs

Cf. A002541, A348388, A348392.

Sequence in context: A086413 A069352 A322832 * A073453 A123229 A127095

Adjacent sequences: A348386 A348387 A348388 * A348390 A348391 A348392

Keyword

nonn,easy,tabf

Author

Wolfdieter Lang, Oct 31 2021

Status

approved