OFFSET
1,2
COMMENTS
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = n/Sum_{k=1..3n} floor(cos^2(Pi*k^(3n)/(3n))). - Anthony Browne, May 24 2016
a(n) = Sum_{d|n} phi(d)*mu(3d)^2. - Ridouane Oudra, Oct 19 2019
From Amiram Eldar, Nov 17 2022: (Start)
Multiplicative with a(3^e) = 1, and a(p^e) = p for p != 3.
Sum_{k=1..n} a(k) ~ c * n^2, where c = (9/22) * Product_{p prime} (1 - 1/(p*(p+1))) = (9/22) * A065463 = 0.2881809... . (End)
MATHEMATICA
Table[n/Sum[Floor[Cos[Pi k^(3 n)/(3 n)]^2], {k, 3 n}], {n, 71}] (* Michael De Vlieger, May 24 2016 *)
a[n_] := Times @@ (First /@ FactorInteger[n])/GCD[n, 3]; Array[a, 100] (* Amiram Eldar, Nov 17 2022 *)
PROG
(PARI) a(n)={factorback(factor(n)[, 1])/gcd(3, n)} \\ Andrew Howroyd, Aug 02 2018
(Sage)
def Gauss_primorial(N, n):
return mul(j for j in (1..N) if gcd(j, n) == 1 and is_prime(j))
def A216913(n): return Gauss_primorial(3*n, 3)/Gauss_primorial(3*n, 3*n)
[A216913(n) for n in (1..80)]
(Magma) [&+[EulerPhi(d)*MoebiusMu(3*d)^2:d in Divisors(n)]:n in [1..70]]; // Marius A. Burtea, Oct 19 2019
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Peter Luschny, Oct 02 2012
STATUS
approved