A067049 Triangle T(n,r) = lcm(n,n-1,n-2,...,n-r+1)/lcm(1,2,3,...,r-1,r), 0 <= r < n.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 2, 1, 1, 5, 10, 10, 5, 1, 1, 6, 15, 10, 5, 1, 1, 1, 7, 21, 35, 35, 7, 7, 1, 1, 8, 28, 28, 70, 14, 14, 2, 1, 1, 9, 36, 84, 42, 42, 42, 6, 3, 1, 1, 10, 45, 60, 210, 42, 42, 6, 3, 1, 1, 1, 11, 55, 165, 330, 462, 462, 66, 33, 11, 11, 1, 1, 12, 66, 110

Offset: 0

Author

Amarnath Murthy, Dec 30 2001

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  1;
  1, 1;
  1, 2, 1;
  1, 3, 3, 1;
  1, 4, 6, 2, 1; ...
		

References

• Amarnath Murthy, Some Notions on Least Common Multiples, Smarandache Notions Journal, Vol. 12, No. 1-2-3, Spring 2001.

Crossrefs

Diagonals give A067046, A067047, A067048. Row sums give A061297.

Programs

Mathematica

t[n_, r_] :=  LCM @@ Table[n-k+1, {k, 1, r}] / LCM @@ Table[k, {k, 1, r}]; t[, 0] = 1; Table[t[n, r], {n, 0, 12}, {r, 0, n}] // Flatten (* _Jean-François Alcover, Apr 22 2014 *)

PARI

t(n, r) = {nt = 1; for (k = n-r+1, n, nt = lcm(nt, k);); dt = 1; for (k = 1, r, dt = lcm(dt, k);); return (nt/dt);} \\ Michel Marcus, Sep 14 2013

Extensions

More terms from Vladeta Jovovic, Dec 31 2001