OFFSET
0,3
COMMENTS
a(n) <> n iff n = 19 * 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 (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1).
FORMULA
Dirichlet g.f.: zeta(s-1)*(1 - 18/19^s). - R. J. Mathar, Apr 18 2011
a(n) = 2*a(n-19) - a(n-38). - G. C. Greubel, Feb 19 2019
From Amiram Eldar, Nov 25 2022: (Start)
Multiplicative with a(19^e) = 19^(e-1), and a(p^e) = p^e if p != 19.
Sum_{k=1..n} a(k) ~ (343/722) * n^2. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 37*log(2)/19. - Amiram Eldar, Sep 08 2023
MAPLE
seq(numer(n/(n+19)), n=0..80); # Muniru A Asiru, Feb 19 2019
MATHEMATICA
f[n_]:=Numerator[n/(n+19)]; Array[f, 100, 0] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2011 *)
PROG
(SageMath) [lcm(n, 19)/19 for n in range(0, 100)] # Zerinvary Lajos, Jun 12 2009
(Magma) [Numerator(n/(n+19)): n in [0..100]]; // Vincenzo Librandi, Apr 18 2011
(PARI) vector(100, n, n--; numerator(n/(n+19))) \\ G. C. Greubel, Feb 19 2019
(GAP) List([0..80], n->NumeratorRat(n/(n+19))); # Muniru A Asiru, Feb 19 2019
CROSSREFS
KEYWORD
nonn,easy,frac,mult
AUTHOR
N. J. A. Sloane, May 15 2005
STATUS
approved