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

1,3

Links

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

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).

Example

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.

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 *)

Prog

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

Crossrefs

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

Cf. A003418, A066574, A038610.

Cf. A173540.

Sequence in context: A319404 A126292 A083265 * A096361 A105045 A205825

Adjacent sequences: A067388 A067389 A067390 * A067392 A067393 A067394

Keyword

nonn

Author

Labos Elemer, Jan 22 2002

Status

approved