A067391 a(n) is the least common multiple of numbers in {1,2,3,...,n-1} which do not divide n.

1, 1, 2, 3, 12, 20, 60, 210, 840, 504, 2520, 27720, 27720, 51480, 360360, 180180, 720720, 4084080, 12252240, 232792560, 232792560, 21162960, 232792560, 5354228880, 5354228880, 2059318800, 26771144400, 80313433200, 80313433200

Offset: 1

Author

Labos Elemer, Jan 22 2002

Keywords

• nonn

Examples

			For n=10: non-divisors = {3,4,6,7,8,9}, lcm(3,4,6,7,8,9) = 8*9*7 = 504 = a(10).
For n=18, a(18) = lcm(4,5,7,8,10,11,12,13,14,15,16,17) = 4084080.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A049820 [count], A007978 [min], A024816 [sum], A055067 [product].

Cf. A003418, A066574, A038610.

Cf. A173540.

Programs

Haskell

a067391 n | n <= 2    = 1
          | otherwise = foldl lcm 1 $ a173540_row n
-- Reinhard Zumkeller, Apr 04 2012

Mathematica

a[n_] := LCM@@Select[Range[1, n-1], Mod[n, # ]!=0& ]
Join[{1,1},Table[LCM@@Complement[Range[n],Divisors[n]],{n,3,30}]] (* Harvey P. Dale, Mar 27 2013 *)

Formula

Let f(n) = lcm(1, 2, ..., n-1) = A003418(n-1). If n = 2*p^k for some prime p, then a(n) = f(n)/p; otherwise a(n) = f(n).