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 A162289 a(n) = 1 if n is relatively prime to 30 else 0. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 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:=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 * A122276 A239199 A265718 Adjacent sequences:  A162286 A162287 A162288 * A162290 A162291 A162292 KEYWORD nonn,mult AUTHOR Michael Somos, Jun 29 2009 STATUS approved

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Last modified September 16 08:30 EDT 2021. Contains 347469 sequences. (Running on oeis4.)