A241475 Triangle t(n,r) = s(n,r)*s(n,r+1), where s(n,r) = lcm(n,n-1,...,n-r+1)/lcm(1,2,...,r-1,r), n >= 1 and 0 <= r < n.

1, 2, 2, 3, 9, 3, 4, 24, 12, 2, 5, 50, 100, 50, 5, 6, 90, 150, 50, 5, 1, 7, 147, 735, 1225, 245, 49, 7, 8, 224, 784, 1960, 980, 196, 28, 2, 9, 324, 3024, 3528, 1764, 1764, 252, 18, 3, 10, 450, 2700, 12600, 8820, 1764, 252, 18, 3, 1, 11, 605, 9075, 54450, 152460, 213444, 30492, 2178, 363, 121, 11

Offset: 1

Author

Jean-François Alcover, Apr 23 2014

Keywords

• nonn
• tabl

Comments

The first eight terms and the first two terms of every row are identical to those of A132812.

Examples

			Triangle begins:
  1;
  2,  2;
  3,  9,   3;
  4, 24,  12,  2;
  5, 50, 100, 50, 5;
  6, 90, 150, 50, 5, 1;
  ...
		

Links

• S. M. Khairnar, Anant W. Vyawahare and J. N. Salunkhe, On Smarandache least common multiple ratio, Scientia Magna Vol. 5 (2009), No. 1, 29-36.
• Amarnath Murthy, Some Notions on Least Common Multiples, Smarandache Notions Journal, Vol. 12, No. 1-2-3, Spring 2001.

Crossrefs

Cf. A067049, A093430, A132812.

Programs

Mathematica

s[, 0] = 1; s[n, r_?NumericQ] := LCM @@ Table[n-k+1, {k, 1, r}] / LCM @@ Table[k, {k, 1, r}]; t[n_, r_] := s[n, r]*s[n, r+1]; Table[t[n, r] , {n, 1, 12}, {r, 0, n-1}] // Flatten