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A162289
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a(n) = 1 if n is relatively prime to 30 else 0.
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0
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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; internal format)
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OFFSET
| 1,1
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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).
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
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EXAMPLE
| x + x^7 + x^11 + x^13 + x^17 + x^19 + x^23 + x^29 + x^31 + x^37 + ...
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PROG
| (PARI) {a(n) = 1 == gcd(30, n)}
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CROSSREFS
| Sequence in context: A014189 A079979 A089010 * A122276 A066288 A111412
Adjacent sequences: A162286 A162287 A162288 * A162290 A162291 A162292
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KEYWORD
| nonn,mult
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AUTHOR
| Michael Somos, Jun 29 2009
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