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%I #43 Apr 27 2021 09:39:22
%S 1,2,2,3,6,3,4,4,12,4,5,10,15,20,5,6,6,6,12,30,6,7,14,21,28,35,42,7,8,
%T 8,24,8,40,24,56,8,9,18,9,36,45,18,63,72,9,10,10,30,20,10,30,70,40,90,
%U 10,11,22,33,44,55,66,77,88,99,110,11,12,12,12,12,60,12,84,24,36,60,132,12
%N Triangular array T read by rows: T(u,v) = lcm(u,v).
%H Reinhard Zumkeller, <a href="/A051173/b051173.txt">Rows n = 1..120 of triangle, flattened</a>
%H Keith Bourque and Steve Ligh, <a href="https://doi.org/10.1016/0024-3795(93)00154-R">Matrices associated with multiplicative functions</a>, Linear Algebra and its Applications 216 (1995) 267-275.
%H Shaofang Hong and Raphael Loewy, <a href="https://doi.org/10.1017/S0017089504001995">Asymptotic behavior of eigenvalues of greatest common divisor matrices</a>, Glasgow Mathematical Journal, Vol. 46, No. 3 (2004) 551-569.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LeastCommonMultiple.html">Least Common Multiple</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Least_common_multiple">Least Common Multiple</a>
%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%F T(n,1) = T(n,n) = n. T(n,2) = A109043(n). - _R. J. Mathar_, Apr 07 2011
%F T(n,k) = A075362(n,k)/A050873(n,k), 1<=k<=n. - _Reinhard Zumkeller_, Apr 25 2011
%F T(n,k) = A051537(n,k) * A050873(n,k). - _Reinhard Zumkeller_, Jul 07 2013
%e Triangle begins:
%e 1;
%e 2, 2;
%e 3, 6, 3;
%e 4, 4, 12, 4;
%e 5, 10, 15, 20, 5;
%e 6, 6, 6, 12, 30, 6;
%e 7, 14, 21, 28, 35, 42, 7;
%e 8, 8, 24, 8, 40, 24, 56, 8;
%p A051173 := proc(u,v) ilcm(u,v) ; end proc: # _R. J. Mathar_, Apr 07 2011
%t Table[LCM[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Jan 30 2018 *)
%o (Haskell)
%o a051173 = lcm
%o a051173_row n = a051173_tabl !! (n-1)
%o a051173_tabl = map (\x -> map (lcm x) [1..x]) [1..]
%o -- _Reinhard Zumkeller_, Aug 13 2013, Jul 07 2013
%o (PARI) T(n,k) = lcm(n,k);
%o tabl(nn) = for (n=1, nn, for (k=1, n, print1(T(n,k), ", ")); print;) \\ _Michel Marcus_, Jul 10 2017
%Y Cf. A003990.
%Y Cf. A051193 (row sums), A000384 (central terms).
%Y Cf. A002260.
%K nonn,easy,tabl
%O 1,2
%A _Clark Kimberling_
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