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A003990 Table of lcm(x,y), read along antidiagonals.

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