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Pairs (i, j) of noncoprime positive integers sorted first by i + j then by i.
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%I #25 Jan 28 2024 10:52:33

%S 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,

%T 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,

%U 10,5,12,3,2,14,4,12,6,10,8,8,10,6,12,4,14,2

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

%C The rows of A290600 interleaved term by term with the reversed rows of A290600. - _Peter Munn_, Jan 28 2024

%H Paolo Xausa, <a href="/A366192/b366192.txt">Table of n, a(n) for n = 1..9886</a>

%e The first few pairs are, seen as an irregular triangle (where rows with a prime index are empty (and are therefore missing)):

%e [2, 2],

%e [2, 4], [3, 3], [4, 2],

%e [2, 6], [4, 4], [6, 2],

%e [3, 6], [6, 3],

%e [2, 8], [4, 6], [5, 5], [6, 4], [ 8, 2],

%e [2, 10], [3, 9], [4, 8], [6, 6], [ 8, 4], [ 9, 3], [10, 2],

%e [2, 12], [4, 10], [6, 8], [7, 7], [ 8, 6], [10, 4], [12, 2],

%e [3, 12], [5, 10], [6, 9], [9, 6], [10, 5], [12, 3],

%e ...

%e There are A016035(n) pairs in row n.

%p aList := proc(upto) local F, P, n, t, count;

%p P := NULL; count := 0:

%p for n from 2 while count < upto do

%p F := select(t -> igcd(t, n - t) <> 1, [$1..n-1]);

%p P := P, seq([t, n - t], t = F);

%p count := count + nops([F]) od:

%p ListTools:-Flatten([P]) end:

%p aList(16);

%t A366192row[n_]:=Select[Array[{#,n-#}&,n-1],!CoprimeQ[First[#],Last[#]]&];

%t Array[A366192row,20,2] (* _Paolo Xausa_, Nov 28 2023 *)

%o (Python)

%o from math import gcd

%o from itertools import chain, count, islice

%o def A366192_gen(): # generator of terms

%o return chain.from_iterable((i,n-i) for n in count(2) for i in range(1,n) if gcd(i,n-i)>1)

%o A366192_list = list(islice(A366192_gen(),30)) # _Chai Wah Wu_, Oct 10 2023

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

%K nonn,look,tabf,easy

%O 1,1

%A _Peter Luschny_, Oct 10 2023