A093430 Triangle read by rows: T(n,k) = lcm(n, n-1, ..., n-k+2, n-k+1)/lcm(1, 2, ..., k) (1 <= k <= n).
1, 2, 1, 3, 3, 1, 4, 6, 2, 1, 5, 10, 10, 5, 1, 6, 15, 10, 5, 1, 1, 7, 21, 35, 35, 7, 7, 1, 8, 28, 28, 70, 14, 14, 2, 1, 9, 36, 84, 42, 42, 42, 6, 3, 1, 10, 45, 60, 210, 42, 42, 6, 3, 1, 1, 11, 55, 165, 330, 462, 462, 66, 33, 11, 11, 1, 12, 66, 110, 165, 66, 462, 66, 33, 11, 11, 1, 1, 13
Offset: 1
Examples
T(7,3) = lcm(7,6,5)/lcm(1,2,3) = 210/6 = 35. Triangle starts: 1; 2, 1; 3, 3, 1; 4, 6, 2, 1; 5, 10, 10, 5, 1; 6, 15, 10, 5, 1, 1; ...
Links
- Bakir Farhi, An analog of the arithmetic triangle obtained by replacing the products by the least common multiples, arXiv:1002.1383 [math.NT], 2010.
- Siao Hong and Guoyou Qian, On the lcm-analog of binomial coefficient, Asian-European Journal of Mathematics, Volume 07, Issue 04, December 2014; DOI: 10.1142/S1793557114500569.
Crossrefs
Programs
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Maple
T:=(n,k)->lcm(seq(i,i=n-k+1..n))/lcm(seq(j,j=1..k)): for n from 1 to 13 do seq(T(n,k),k=1..n) od; # yields sequence in triangular form # Emeric Deutsch, Jan 30 2006
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Mathematica
t[n_, k_] := LCM @@ Table[j, {j, n-k+1, n}] / LCM @@ Table[j, {j, 1, k}]; t[, 0] = 1; Table[t[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* _Jean-François Alcover, Apr 23 2014 *)
Extensions
More terms from Emeric Deutsch, Jan 30 2006
Comments