A216913 a(n) = Gauss_primorial(3*n, 3) / Gauss_primorial(3*n, 3*n).
1, 2, 1, 2, 5, 2, 7, 2, 1, 10, 11, 2, 13, 14, 5, 2, 17, 2, 19, 10, 7, 22, 23, 2, 5, 26, 1, 14, 29, 10, 31, 2, 11, 34, 35, 2, 37, 38, 13, 10, 41, 14, 43, 22, 5, 46, 47, 2, 7, 10, 17, 26, 53, 2, 55, 14, 19, 58, 59, 10, 61, 62, 7, 2, 65, 22, 67, 34, 23, 70, 71
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1000
Programs
-
Magma
[&+[EulerPhi(d)*MoebiusMu(3*d)^2:d in Divisors(n)]:n in [1..70]]; // Marius A. Burtea, Oct 19 2019
-
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 *) -
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)]
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)
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