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

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, 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, 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

Offset

1,2

Comments

A(x,x) = x on the diagonal. - Reinhard Zumkeller, Aug 05 2012

Links

T. D. Noe, First 100 antidiagonals of array, flattened

Kival Ngaokrajang, Illustration of pattern, where terms with least significant decimal digit equal to zero are colored.

Index entries for sequences related to lcm's

Example

The symmetric array is lcm(x,y) = lcm(y,x):
   1  2  3  4  5  6  7  8  9 10 ...
   2  2  6  4 10  6 14  8 18 10 ...
   3  6  3 12 15  6 21 24  9 30 ...
   4  4 12  4 20 12 28  8 36 20 ...
   5 10 15 20  5 30 35 40 45 10 ...
   6  6  6 12 30  6 42 24 18 30 ...
   7 14 21 28 35 42  7 56 63 70 ...
   8  8 24  8 40 24 56  8 72 40 ...
   9 18  9 36 45 18 63 72  9 90 ...
  10 10 30 20 10 30 70 40 90 10 ...

Mathematica

Table[ LCM[x-y, y], {x, 1, 14}, {y, 1, x-1}] // Flatten (* Jean-François Alcover, Aug 20 2013 *)

Prog

(Haskell)
a003990 x y = a003990_adiag x !! (y-1)
a003990_adiag n = a003990_tabl !! (n-1)
a003990_tabl = zipWith (zipWith lcm) a002260_tabl $ map reverse a002260_tabl
-- Reinhard Zumkeller, Aug 05 2012
(PARI) A(x, y)=lcm(x, y) \\ Charles R Greathouse IV, Feb 06 2017

Crossrefs

Cf. A003989, A003991, A051173.

A(x, y) = A075174(A003986(A075173(x), A075173(y))) = A075176(A003986(A075175(x), A075175(y))).

Antidiagonal sums are in A006580.

Cf. A002260.

Sequence in context: A045772 A294977 A091256 * A287958 A308630 A059896

Adjacent sequences: A003987 A003988 A003989 * A003991 A003992 A003993

Keyword

tabl,nonn,easy,nice,look

Author

Marc LeBrun

Status

approved