A348390 - OEIS

A348390

Irregular triangle read by rows: for n >= 2 the row members a(n, m) give the proper divisors of k, followed by the multiples of k larger than k and not exceeding n, for k = 1, 2, ..., n.

2, 1, 2, 3, 1, 1, 2, 3, 4, 1, 4, 1, 1, 2, 2, 3, 4, 5, 1, 4, 1, 1, 2, 1, 2, 3, 4, 5, 6, 1, 4, 6, 1, 6, 1, 2, 1, 1, 2, 3, 2, 3, 4, 5, 6, 7, 1, 4, 6, 1, 6, 1, 2, 1, 1, 2, 3, 1, 2, 3, 4, 5, 6, 7, 8, 1, 4, 6, 8, 1, 6, 1, 2, 8, 1, 1, 2, 3, 1, 1, 2, 4

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,1

COMMENTS

The length of row n is 2*A002541(n), for n >= 2.

The sum of row n is A348391(n). The sum of the proper divisors of row n is A153485(n). The sum of the multiples in row n is A348392(n). Hence, A348391(n) = A153485(n) + A348392(n).

For k = 1 the proper divisor set is empty, and for k > floor(n/2) the set of multiples is empty.

LINKS

Table of n, a(n) for n=2..83.

FORMULA

For n >= 2 row n gives the sequence of the sequence d(n, k) of proper divisors of k (A027751(k)) followed by the sequences m(n, k) of the multiples of k, larger than k and not exceeding n (A348389), for k = 1, 2, 3, ..., n.

EXAMPLE

The irregular triangle a(n, m), m = 1, 2, ..., 2*A002541(n) begins:

(members for k = 1, 2, ..., n are separated by a vertical bar, and the proper divisors and multiples are separated by a comma)

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 25 26 27 28 ...

-----------------------------------------------------------------------------------

2: 2|1

3: 2 3|1|1

4: 2 3 4|1,4|1|1 2

5: 2 3 4 5|1,4|1|1 2| 1

6: 2 3 4 5 6|1,4 6| 1, 6| 1 2| 1| 1 2 3

7: 2 3 4 5 6 7|1,4 6| 1, 6| 1 2| 1| 1 2 3| 1

8: 3 4 5 6 7 8|1,4 6 8| 1 ,6| 1 2 ,8| 1| 1 2 3| 1| 1 2 4

9: 2 3 4 5 6 7 8 9| 1, 4 6 8| 1, 6 9| 1 2, 8| 1| 1 2 3| 1| 1 2 4| 1 3

...

n = 10: 2 3 4 5 6 7 8 9 10 | 1, 4 6 8 10 | 1, 6 9 | 1 2, 8 | 1, 10 | 1 2 3 | 1 | 1 2 4 | 1 3 | 1 2 5

-----------------------------------------------------------------------------------

n = 4: d(4, 1) = {}, m(4, 1) = {2, 3, 4}; d(4, 2) = {1}, m(4, 2) = {4}; d(4, 3) = {1}, m(4, 3) = {}; d(4, 4) = {1, 2}, m(4, 4) = {}, This explains row n = 4.

MATHEMATICA

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

CROSSREFS

Cf. A002541, A027751, A153485, A348389, A348391, A348392.

Sequence in context: A277822 A327616 A181631 * A133674 A348245 A215026

Adjacent sequences: A348387 A348388 A348389 * A348391 A348392 A348393

KEYWORD

nonn,easy,tabf

AUTHOR

Wolfdieter Lang, Nov 07 2021

STATUS

approved

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.