A348554 Irregular triangle read by rows: row n gives the divisors d of 2*n with 1 < d < 2*n, for n >= 2.

2, 2, 3, 2, 4, 2, 5, 2, 3, 4, 6, 2, 7, 2, 4, 8, 2, 3, 6, 9, 2, 4, 5, 10, 2, 11, 2, 3, 4, 6, 8, 12, 2, 13, 2, 4, 7, 14, 2, 3, 5, 6, 10, 15, 2, 4, 8, 16, 2, 17, 2, 3, 4, 6, 9, 12, 18, 2, 19, 2, 4, 5, 8, 10, 20, 2, 3, 6, 7, 14, 21, 2, 4, 11, 22, 2, 23, 2, 3, 4, 6, 8, 12, 16, 24, 2, 5, 10, 25

Offset: 2

Author

Wolfdieter Lang, Oct 22 2021

Keywords

• nonn
• tabf

Comments

This gives the rows 2*n of A137510, for n >= 2.

The length of row n is A069930(n) = tau(2*n) - 2 = A099777(n) - 2.

The sum of row n is A346880(n) = A062731(n) - (2*n + 1).

Examples

			The irregular triangle T(n, k) begins:
n, 2*n / k 1  2  3  4  5  6  7 ...
----------------------------------
2,   4:    2
3,   6:    2  3
4,   8:    2  4
5,  10:    2  5
6   12:    2  3  4 6
7,  14:    2  7
8,  16:    2  4  8
9,  18:    2  3  6  9
10, 20:    2  4  5 10
11, 22:    2 11
12, 24:    2  3  4  6  8 12
13, 26:    2 13
14, 28:    2  4  7 14
15, 30:    2  3  5  6 10 15
16, 32:    2  4  8  1
17, 34:    2 17
18, 36:    2  3  4  6  9 12 18
19, 38:    2 19
20, 40:    2  4  5  8 10 20
...
		

Crossrefs

Cf. A069930, A099777, A137510, A346880.

Programs

Mathematica

Flatten@Table[Select[Divisors[2n],1<#<2n&],{n,2,25}] (* Giorgos Kalogeropoulos, Oct 22 2021 *)

PARI

row(n) = select(x->((x>1) && (x<2*n)), divisors(2*n)); \\ Michel Marcus, Oct 23 2021

Formula

T(n, k) = A137510(2*n, k), for n >= 2 and k = 1, 2, ..., A069930(n).