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

Author

Marc LeBrun

Keywords

• tabl
• nonn
• easy
• nice
• look

Comments

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

Examples

			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 ...
		

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

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.

Programs

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

Mathematica

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

PARI

A(x,y)=lcm(x,y) \\ Charles R Greathouse IV, Feb 06 2017