A366192 Pairs (i, j) of noncoprime positive integers sorted first by i + j then by i.

2, 2, 2, 4, 3, 3, 4, 2, 2, 6, 4, 4, 6, 2, 3, 6, 6, 3, 2, 8, 4, 6, 5, 5, 6, 4, 8, 2, 2, 10, 3, 9, 4, 8, 6, 6, 8, 4, 9, 3, 10, 2, 2, 12, 4, 10, 6, 8, 7, 7, 8, 6, 10, 4, 12, 2, 3, 12, 5, 10, 6, 9, 9, 6, 10, 5, 12, 3, 2, 14, 4, 12, 6, 10, 8, 8, 10, 6, 12, 4, 14, 2

Offset: 1

Author

Peter Luschny, Oct 10 2023

Keywords

• nonn
• look
• tabf
• easy

Comments

The rows of A290600 interleaved term by term with the reversed rows of A290600. - Peter Munn, Jan 28 2024

Examples

			The first few pairs are, seen as an irregular triangle (where rows with a prime index are empty (and are therefore missing)):
  [2,  2],
  [2,  4], [3,  3], [4, 2],
  [2,  6], [4,  4], [6, 2],
  [3,  6], [6,  3],
  [2,  8], [4,  6], [5, 5], [6, 4], [ 8, 2],
  [2, 10], [3,  9], [4, 8], [6, 6], [ 8, 4], [ 9, 3], [10, 2],
  [2, 12], [4, 10], [6, 8], [7, 7], [ 8, 6], [10, 4], [12, 2],
  [3, 12], [5, 10], [6, 9], [9, 6], [10, 5], [12, 3],
  ...
There are A016035(n) pairs in row n.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..9886

Crossrefs

Cf. A016035, A290600 (first bisection), A352911 (complement).

Programs

Maple

aList := proc(upto) local F, P, n, t, count;
P := NULL; count := 0:
for n from 2 while count < upto do
    F := select(t -> igcd(t, n - t) <> 1, [$1..n-1]);
    P := P, seq([t, n - t], t = F);
    count := count + nops([F]) od:
ListTools:-Flatten([P]) end:
aList(16);

Mathematica

A366192row[n_]:=Select[Array[{#,n-#}&,n-1],!CoprimeQ[First[#],Last[#]]&];
Array[A366192row,20,2] (* Paolo Xausa, Nov 28 2023 *)

Python

from math import gcd
from itertools import chain, count, islice
def A366192_gen(): # generator of terms
    return chain.from_iterable((i,n-i) for n in count(2) for i in range(1,n) if gcd(i,n-i)>1)
A366192_list = list(islice(A366192_gen(),30)) # Chai Wah Wu, Oct 10 2023