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

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, 105, 126, 9, 24, 16, 72, 12, 120, 48, 168, 10, 27, 54, 15, 108, 135, 30, 189, 216, 11, 30, 20, 90, 40, 14, 60, 210, 80, 270, 12, 33, 66, 99, 132, 165, 198, 231, 264, 297, 330, 13

Offset: 1

Author

Michel Marcus, May 08 2014

Keywords

• nonn
• tabl

Comments

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.

If gcd(n,k)+2 is replaced by gcd(n,k), then triangle A051173 is obtained.

Examples

			Triangle begins:
   3;
   6,  4;
   9, 18,  5;
  12,  8, 36,  6;
  15, 30, 45, 60,  7;
  18, 12, 10, 24, 90,  8;
  ...
		

Links

• Indranil Ghosh, Rows 1..100 of triangle, flattened
• Ana Rechtman, Mai, 1er défi, Images des Mathématiques, CNRS, 2014 (in French).
• See also Comments, Images des Mathématiques, CNRS, 2014.

Programs

Mathematica

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 *)

PARI

tabl(nn) = {for (n=1, nn, for (k=1, n, print1(n*k*(gcd(n,k)+2)/gcd(n,k)^2, ", ");); print(););}