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A051173 Triangular array T read by rows: T(u,v) = lcm(u,v). 13

%I

%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

%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, Steve Ligh, <a href="http://dx.doi.org/10.1016/0024-3795(93)00154-R">Matrices associated with multiplicative functions</a>, Lin. Alg. Applic. 216 (1995) 265-275

%H Shaofang Hong, Raphael Loewy, <a href="http://dx.doi.org/10.1017/S0017089504001995">Asymptotic behavior of eigenvalues of greatest common divisor matrices</a>, Glasgow Math. J. 46 (2004) 551-569

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LeastCommonMultiple.html">Least Common Multiple</a>

%H Wikipedia, <a href="http://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-Fran├žois 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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Last modified June 26 04:11 EDT 2019. Contains 324369 sequences. (Running on oeis4.)