A106619 a(n) = numerator of n/(n+18).

0, 1, 1, 1, 2, 5, 1, 7, 4, 1, 5, 11, 2, 13, 7, 5, 8, 17, 1, 19, 10, 7, 11, 23, 4, 25, 13, 3, 14, 29, 5, 31, 16, 11, 17, 35, 2, 37, 19, 13, 20, 41, 7, 43, 22, 5, 23, 47, 8, 49, 25, 17, 26, 53, 3, 55, 28, 19, 29, 59, 10, 61, 31, 7, 32, 65, 11, 67, 34, 23, 35, 71, 4, 73, 37, 25, 38, 77, 13, 79

Offset: 0

Author

N. J. A. Sloane, May 15 2005

Keywords

• nonn
• easy
• frac
• mult

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).

Crossrefs

Cf. Sequences given by the formula numerator(n/(n + k)): A026741 (k = 2), A051176 (k = 3), A060819 (k = 4), A060791 (k = 5), A060789 (k = 6), A106608 thru A106612 (k = 7 thru 11), A051724 (k = 12), A106614 thru A106621 (k = 13 thru 20).

Cf. A227042.

Programs

GAP

List([0..80],n->NumeratorRat(n/(n+18))); # Muniru A Asiru, Feb 19 2019

Magma

[Numerator(n/(n+18)): n in [0..100]]; // Vincenzo Librandi, Apr 18 2011

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 *)

PARI

vector(100, n, n--; numerator(n/(n+18))) \\ G. C. Greubel, Feb 19 2019

Sage

[lcm(n,18)/18 for n in range(0, 100)] # Zerinvary Lajos, Jun 12 2009

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)