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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). 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
An LCM-analog of the binomial coefficients. - N. J. A. Sloane, Aug 26 2015
LINKS
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.
EXAMPLE
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;
...
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
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 *)
CROSSREFS
Cf. A067049 (same triangle with an additional leading column of ones).
Row sums yield A093431.
Sequence in context: A090349 A157379 A212139 * A074659 A131251 A144400
KEYWORD
nonn,tabl
AUTHOR
Amarnath Murthy, Mar 31 2004
EXTENSIONS
More terms from Emeric Deutsch, Jan 30 2006
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)