%I #34 Apr 01 2018 18:10:19
%S 1,2,2,3,2,3,4,6,6,4,5,4,3,4,5,6,10,12,12,10,6,7,6,15,4,15,6,7,8,14,6,
%T 20,20,6,14,8,9,8,21,12,5,12,21,8,9,10,18,24,28,30,30,28,24,18,10,11,
%U 10,9,8,35,6,35,8,9,10,11,12,22,30,36,40,42,42,40,36,30,22,12,13,12,33,20,45,24
%N Table of lcm(x,y), read along antidiagonals.
%C A(x,x) = x on the diagonal. - _Reinhard Zumkeller_, Aug 05 2012
%H T. D. Noe, <a href="/A003990/b003990.txt">First 100 antidiagonals of array, flattened</a>
%H Kival Ngaokrajang, <a href="/A003990/a003990.pdf">Illustration of pattern</a>, where terms with least significant decimal digit equal to zero are colored.
%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>
%e The symmetric array is lcm(x,y) = lcm(y,x):
%e 1 2 3 4 5 6 7 8 9 10 ...
%e 2 2 6 4 10 6 14 8 18 10 ...
%e 3 6 3 12 15 6 21 24 9 30 ...
%e 4 4 12 4 20 12 28 8 36 20 ...
%e 5 10 15 20 5 30 35 40 45 10 ...
%e 6 6 6 12 30 6 42 24 18 30 ...
%e 7 14 21 28 35 42 7 56 63 70 ...
%e 8 8 24 8 40 24 56 8 72 40 ...
%e 9 18 9 36 45 18 63 72 9 90 ...
%e 10 10 30 20 10 30 70 40 90 10 ...
%t Table[ LCM[x-y, y], {x, 1, 14}, {y, 1, x-1}] // Flatten (* _Jean-François Alcover_, Aug 20 2013 *)
%o (Haskell)
%o a003990 x y = a003990_adiag x !! (y-1)
%o a003990_adiag n = a003990_tabl !! (n-1)
%o a003990_tabl = zipWith (zipWith lcm) a002260_tabl $ map reverse a002260_tabl
%o -- _Reinhard Zumkeller_, Aug 05 2012
%o (PARI) A(x,y)=lcm(x,y) \\ _Charles R Greathouse IV_, Feb 06 2017
%Y Cf. A003989, A003991, A051173.
%Y A(x, y) = A075174(A003986(A075173(x), A075173(y))) = A075176(A003986(A075175(x), A075175(y))).
%Y Antidiagonal sums are in A006580.
%Y Cf. A002260.
%K tabl,nonn,easy,nice,look
%O 1,2
%A _Marc LeBrun_