OFFSET
0,5
COMMENTS
a(n+3), n >= 0, is the denominator of the harmonic mean H(n,3) = 6*n/(n+3). a(n+3) = (n+3)/gcd(n+3,18). - Wolfdieter Lang, Jul 04 2013
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1).
FORMULA
a(n) = 2*a(n-18) - a(n-36). - Paul Curtz, Feb 27 2011
Nonasection: a(9*n) = A026741(n). - Paul Curtz, Mar 21 2011
Dirichlet g.f.: zeta(s-1)*(1 - 2/3^s - 2/9^s - 1/2^s + 2/6^s + 2/18^s). - R. J. Mathar, Apr 18 2011
a(n) = n/gcd(n,18), n >= 0. See the harmonic mean comment above, and the Zerinvary Lajos program below. - Wolfdieter Lang, Jul 04 2013
a(n+3) = A227042(n+3,3), n >= 0. - Wolfdieter Lang, Jul 04 2013
From Amiram Eldar, Nov 25 2022: (Start)
Multiplicative with a(2^e) = 2^max(0, e-1), a(3^e) = 3^max(0,e-2), and a(p^e) = p^e otherwise.
Sum_{k=1..n} a(k) ~ (61/216) * n^2. (End)
MAPLE
seq(numer(n/(n+18)), n=0..80); # Muniru A Asiru, Feb 19 2019
MATHEMATICA
f[n_]:=Numerator[n/(n+18)]; Array[f, 100, 0] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2011 *)
PROG
(Sage) [lcm(n, 18)/18 for n in range(0, 100)] # Zerinvary Lajos, Jun 12 2009
(Magma) [Numerator(n/(n+18)): n in [0..100]]; // Vincenzo Librandi, Apr 18 2011
(PARI) vector(100, n, n--; numerator(n/(n+18))) \\ G. C. Greubel, Feb 19 2019
(GAP) List([0..80], n->NumeratorRat(n/(n+18))); # Muniru A Asiru, Feb 19 2019
CROSSREFS
KEYWORD
nonn,easy,frac,mult
AUTHOR
N. J. A. Sloane, May 15 2005
STATUS
approved