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A109042 Square array read by antidiagonals: A(n, k) = lcm(n, k) for n >= 0, k >= 0.

%I A109042 #26 Mar 24 2025 19:45:59
%S A109042 0,0,0,0,1,0,0,2,2,0,0,3,2,3,0,0,4,6,6,4,0,0,5,4,3,4,5,0,0,6,10,12,12,
%T A109042 10,6,0,0,7,6,15,4,15,6,7,0,0,8,14,6,20,20,6,14,8,0,0,9,8,21,12,5,12,
%U A109042 21,8,9,0,0,10,18,24,28,30,30,28,24,18,10,0,0,11,10,9,8,35,6,35,8,9,10,11,0
%N A109042 Square array read by antidiagonals: A(n, k) = lcm(n, k) for n >= 0, k >= 0.
%H A109042 Alois P. Heinz, <a href="/A109042/b109042.txt">Antidiagonals n = 0..140, flattened</a>
%F A109042 lcm(n, k) = n*k / gcd(n, k) for (n, k) != (0, 0).
%e A109042 Seen as an array:
%e A109042   [0] 0, 0,  0,  0,  0,  0,  0,  0,  0,  0, ...
%e A109042   [1] 0, 1,  2,  3,  4,  5,  6,  7,  8,  9, ...
%e A109042   [2] 0, 2,  2,  6,  4, 10,  6, 14,  8, 18, ...
%e A109042   [3] 0, 3,  6,  3, 12, 15,  6, 21, 24,  9, ...
%e A109042   [4] 0, 4,  4, 12,  4, 20, 12, 28,  8, 36, ...
%e A109042   [5] 0, 5, 10, 15, 20,  5, 30, 35, 40, 45, ...
%e A109042   [6] 0, 6,  6,  6, 12, 30,  6, 42, 24, 18, ...
%e A109042   [7] 0, 7, 14, 21, 28, 35, 42,  7, 56, 63, ...
%e A109042   [8] 0, 8,  8, 24,  8, 40, 24, 56,  8, 72, ...
%e A109042   [9] 0, 9, 18,  9, 36, 45, 18, 63, 72,  9, ...
%e A109042 .
%e A109042 Seen as a triangle T(n, k) = lcm(n - k, k).
%e A109042   [0] 0;
%e A109042   [1] 0, 0;
%e A109042   [2] 0, 1,  0;
%e A109042   [3] 0, 2,  2,  0;
%e A109042   [4] 0, 3,  2,  3,  0;
%e A109042   [5] 0, 4,  6,  6,  4,  0;
%e A109042   [6] 0, 5,  4,  3,  4,  5, 0;
%e A109042   [7] 0, 6, 10, 12, 12, 10, 6,  0;
%e A109042   [8] 0, 7,  6, 15,  4, 15, 6,  7, 0;
%e A109042   [9] 0, 8, 14,  6, 20, 20, 6, 14, 8, 0;
%p A109042 T := (n, k) -> ilcm(n - k, k):
%p A109042 for n from 0 to 9 do seq(T(n, k), k = 0..n) od;  # _Peter Luschny_, Mar 24 2025
%Y A109042 Rows A000027, A109043, A109044, A109045, A109046, A109047, A109048, A109049, A109050, A109051, A109052, A109053, A006580 (row sums of triangle), A001477 (main diagonal, central terms).
%Y A109042 Variants: A003990 is (1, 1) based, A051173 (T(n,k) = lcm(n,k)).
%K A109042 nonn,easy,tabl
%O A109042 0,8
%A A109042 _Mitch Harris_, Jun 18 2005