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

1,1

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.

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.

Example

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

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 *)

Prog

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

Crossrefs

Sequence in context: A083349 A065230 A316478 * A294671 A275985 A163294

Adjacent sequences: A242221 A242222 A242223 * A242225 A242226 A242227

Keyword

nonn,tabl

Author

Michel Marcus, May 08 2014

Status

approved