A067391 - OEIS

%I #19 Mar 25 2020 10:42:20

%S 1,1,2,3,12,20,60,210,840,504,2520,27720,27720,51480,360360,180180,

%T 720720,4084080,12252240,232792560,232792560,21162960,232792560,

%U 5354228880,5354228880,2059318800,26771144400,80313433200,80313433200

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

%H Reinhard Zumkeller, <a href="/A067391/b067391.txt">Table of n, a(n) for n = 1..1000</a>

%F 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).

%e For n=10: non-divisors = {3,4,6,7,8,9}, lcm(3,4,6,7,8,9) = 8*9*7 = 504 = a(10).

%e For n=18, a(18) = lcm(4,5,7,8,10,11,12,13,14,15,16,17) = 4084080.

%t a[n_] := LCM@@Select[Range[1, n-1], Mod[n, # ]!=0& ]

%t Join[{1,1},Table[LCM@@Complement[Range[n],Divisors[n]],{n,3,30}]] (* _Harvey P. Dale_, Mar 27 2013 *)

%o (Haskell)

%o a067391 n | n <= 2    = 1

%o           | otherwise = foldl lcm 1 $ a173540_row n

%o -- _Reinhard Zumkeller_, Apr 04 2012

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

%Y Cf. A003418, A066574, A038610.

%Y Cf. A173540.

%K nonn

%O 1,3

%A _Labos Elemer_, Jan 22 2002