OFFSET
0,3
COMMENTS
a(n) <> n iff n = 17 * k, in this case, a(n) = k. - Bernard Schott, Feb 19 2019
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1).
FORMULA
Dirichlet g.f.: zeta(s-1)*(1 - 16/17^s). - R. J. Mathar, Apr 18 2011
a(n) = 2*a(n-17) - a(n-34). - G. C. Greubel, Feb 19 2019
From Amiram Eldar, Nov 25 2022: (Start)
Multiplicative with a(17^e) = 17^(e-1), and a(p^e) = p^e if p != 17.
Sum_{k=1..n} a(k) ~ (273/578) * n^2. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 33*log(2)/17. - Amiram Eldar, Sep 08 2023
MAPLE
seq(numer(n/(n+17)), n=0..80); # Muniru A Asiru, Feb 19 2019
MATHEMATICA
f[n_]:=Numerator[n/(n+17)]; Array[f, 100, 0] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2011 *)
PROG
(Sage) [lcm(n, 17)/17 for n in range(0, 100)] # Zerinvary Lajos, Jun 12 2009
(Magma) [Numerator(n/(n+17)): n in [0..100]]; // Vincenzo Librandi, Apr 18 2011
(PARI) vector(100, n, n--; numerator(n/(n+17))) \\ G. C. Greubel, Feb 19 2019
(GAP) List([0..80], n->NumeratorRat(n/(n+17))); # Muniru A Asiru, Feb 19 2019
CROSSREFS
KEYWORD
nonn,easy,frac,mult
AUTHOR
N. J. A. Sloane, May 15 2005
STATUS
approved