OFFSET
0,2
COMMENTS
Exponent of the dihedral group D(2n) = <x, y | x^n = y^2 = 1, yxy = x^-1>. - Arkadiusz Wesolowski, Sep 10 2013
Second column of table A210530. - Boris Putievskiy, Jan 29 2013
For n > 1, the basic period of A000166(k) (mod n) (Miska, 2016). - Amiram Eldar, Mar 03 2021
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Dorin Andrica, Sorin Rădulescu, and George Cătălin Ţurcaş, The Exponent of a Group: Properties, Computations and Applications, Disc. Math. and Applications, Springer, Cham (2020), 57-108.
Piotr Miska, Arithmetic properties of the sequence of derangements, Journal of Number Theory, Vol. 163 (2016), pp. 114-145; arXiv preprint, arXiv:1508.01987 [math.NT], 2015. See p. 124 (p. 14 in the preprint).
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
FORMULA
a(n) = n*2 / gcd(n, 2).
a(n) = -(n*((-1)^n-3))/2. - Stephen Crowley, Feb 11 2007
From R. J. Mathar, Aug 20 2008: (Start)
a(n) = A066043(n), n > 1.
a(n) = 2*A026741(n).
G.f.: 2*x(1+x+x^2)/((1-x)^2*(1+x)^2). (End)
a(n) = n*A000034(n). - Paul Curtz, Mar 25 2011
E.g.f.: x*(2*cosh(x) + sinh(x)). - Stefano Spezia, May 09 2021
Sum_{k=1..n} a(k) ~ (3/4) * n^2. - Amiram Eldar, Nov 26 2022
MATHEMATICA
LCM[Range[0, 70], 2] (* Harvey P. Dale, Aug 19 2012 *)
PROG
(Sage) [lcm(n, 2) for n in range(0, 68)] # Zerinvary Lajos, Jun 07 2009
(Haskell)
a109043 = (lcm 2)
a109043_list = zipWith (*) [0..] a000034_list
-- Reinhard Zumkeller, Mar 31 2012
(Magma) [0, 2, 2] cat [Exponent(DihedralGroup(n)) : n in [3..65]]; // Arkadiusz Wesolowski, Sep 10 2013
(PARI) a(n)=lcm(n, 2) \\ Charles R Greathouse IV, Sep 24 2015
(Python)
def A109043(n): return n<<1 if n&1 else n # Chai Wah Wu, Aug 05 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mitch Harris, Jun 18 2005
STATUS
approved