A162289 a(n) = 1 if n is relatively prime to 30 else 0.

1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Formula

Euler transform of length 30 sequence [0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1].

Moebius transform is length 30 sequence [1, -1, -1, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1].

a(n) is multiplicative with a(2^e) = a(3^e) = a(5^e) = 0^e, a(p^e) = 1 if p>5.

a(n) = a(n + 30) = a(-n) for all n in Z.

G.f.: x * (1 + x^6) * (1 + x^10) * (1 + x^12) / (1 - x^30).

Dirichlet g.f.: zeta(s)*(1-1/2^s)*(1-1/3^s)*(1-1/5^s). - R. J. Mathar, Jun 01 2011

Asymptotic mean: lim_{n->oo} (1/n) * Sum_{k=1..n} = 4/15. - Amiram Eldar, Dec 06 2020

Example

G.f. = x + x^7 + x^11 + x^13 + x^17 + x^19 + x^23 + x^29 + x^31 + x^37 + ...

Mathematica

Boole[CoprimeQ[Range[110], 30]] (* Harvey P. Dale, Jul 11 2017 *)

Prog

(PARI) {a(n) = 1 == gcd(30, n)};
(PARI) x='x+O('x^100); Vec(x*(1+x^6)*(1+x^10)*(1+x^12)/(1-x^30)) \\ G. C. Greubel, Sep 25 2018
(Magma) m:=100; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+x^6)*(1+x^10)*(1+x^12)/(1-x^30))); // G. C. Greubel, Sep 25 2018

Crossrefs

Sequence in context: A288711 A347312 A089010 * A373139 A122276 A352679

Adjacent sequences: A162286 A162287 A162288 * A162290 A162291 A162292

Keyword

nonn,mult

Author

Michael Somos, Jun 29 2009

Status

approved