%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