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A242224 Triangular array T read by rows, T(n, k) = n*k*(gcd(n,k)+2)/gcd(n,k)^2.

%I A242224 #20 Oct 19 2024 15:57:32
%S A242224 3,6,4,9,18,5,12,8,36,6,15,30,45,60,7,18,12,10,24,90,8,21,42,63,84,
%T A242224 105,126,9,24,16,72,12,120,48,168,10,27,54,15,108,135,30,189,216,11,
%U A242224 30,20,90,40,14,60,210,80,270,12,33,66,99,132,165,198,231,264,297,330,13
%N A242224 Triangular array T read by rows, T(n, k) = n*k*(gcd(n,k)+2)/gcd(n,k)^2.
%C A242224 Described in the CNRS link as a puzzle where op(n,k) is defined by: op(n,n)=n+2, op(n,k)=op(k,n) and op(n,n+k)/op(n,k)=(n+k)/k.
%C A242224 If gcd(n,k)+2 is replaced by gcd(n,k), then triangle A051173 is obtained.
%H A242224 Indranil Ghosh, <a href="/A242224/b242224.txt">Rows 1..100 of triangle, flattened</a>
%H A242224 Ana Rechtman, <a href="http://images-archive.math.cnrs.fr/Mai-1er-defi.html">Mai, 1er défi</a>, Images des Mathématiques, CNRS, 2014 (in French).
%H A242224 See also <a href="http://images-archive.math.cnrs.fr/spip.php?page=forum&amp;id_article=2583">Comments</a>, Images des Mathématiques, CNRS, 2014.
%e A242224 Triangle begins:
%e A242224    3;
%e A242224    6,  4;
%e A242224    9, 18,  5;
%e A242224   12,  8, 36,  6;
%e A242224   15, 30, 45, 60,  7;
%e A242224   18, 12, 10, 24, 90,  8;
%e A242224   ...
%t A242224 t[n_, k_] := n*k*(GCD[n, k] +2)/GCD[n, k]^2; Table[ t[n, k], {n, 12}, {k, n}] // Flatten (* _Robert G. Wilson v_, Jan 21 2018 *)
%o A242224 (PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, print1(n*k*(gcd(n,k)+2)/gcd(n,k)^2, ", ");); print(););}
%K A242224 nonn,tabl
%O A242224 1,1
%A A242224 _Michel Marcus_, May 08 2014