OFFSET
0,3
COMMENTS
Multiplicative and also a strong divisibility sequence: gcd(a(n),a(m)) = a(gcd(n,m)) for n, m >= 1. - Peter Bala, Feb 24 2019
LINKS
Nathaniel Johnston, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1).
FORMULA
Dirichlet g.f.: zeta(s-1)*(1-4/5^s-2/3^s+8/15^s). - R. J. Mathar, Apr 18 2011
a(n) = gcd((n-2)*(n-1)*n*(n+1)*(n+2)/15, n) for n>=1. - Lechoslaw Ratajczak, Feb 19 2017
From Peter Bala, Feb 24 2019: (Start)
a(n) = n/gcd(n,15), a quasi-polynomial in n since gcd(n,15) is a purely periodic sequence of period 15.
O.g.f.: F(x) - 2*F(x^3) - 4*F(x^5) + 8*F(x^15), where F(x) = x/(1 - x)^2.
O.g.f. for reciprocals: Sum_{n >= 1} x^n/a(n) = Sum_{d divides 15} (phi(d)/d) * log(1/(1 - x^d)) = log(1/(1 - x)) + (2/3)*log(1/(1 - x^3)) + (4/5)*log(1/(1 - x^5)) + (8/15)*log(1/(1 - x^15)), where phi(n) denotes the Euler totient function A000010. (End)
From Amiram Eldar, Nov 25 2022: (Start)
Multiplicative with a(3^e) = 3^max(0,e-1), a(5^e) = 5^max(0,e-1), and a(p^e) = p^e otherwise.
Sum_{k=1..n} a(k) ~ (49/150) * n^2. (End)
MAPLE
seq(numer(n/(n+15)), n=0..100); # Nathaniel Johnston, Apr 18 2011
MATHEMATICA
f[n_]:=Numerator[n/(n+15)]; Array[f, 100, 0] (* Vladimir Joseph Stephan Orlovsky, Feb 17 2011*)
PROG
(Sage) [lcm(n, 15)/15 for n in range(0, 79)] # Zerinvary Lajos, Jun 09 2009
(Magma) [Numerator(n/(n+15)): n in [0..100]]; // Vincenzo Librandi, Apr 18 2011
(PARI) a(n) = numerator(n/(n+15)); \\ Michel Marcus, Feb 19 2017
(GAP) List([0..80], n->NumeratorRat(n/(n+15))); # Muniru A Asiru, Feb 19 2019
CROSSREFS
KEYWORD
nonn,easy,frac,mult
AUTHOR
N. J. A. Sloane, May 15 2005
STATUS
approved