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A086798
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Number of coefficients equal to zero in n-th cyclotomic polynomial.
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2
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0, 0, 0, 1, 0, 0, 0, 3, 4, 0, 0, 2, 0, 0, 2, 7, 0, 4, 0, 4, 4, 0, 0, 6, 16, 0, 16, 6, 0, 2, 0, 15, 6, 0, 8, 10, 0, 0, 8, 12, 0, 4, 0, 10, 18, 0, 0, 14, 36, 16, 10, 12, 0, 16, 24, 18, 12, 0, 0, 10, 0, 0, 28, 31, 18, 6, 0, 16, 14, 8, 0, 22, 0, 0, 34, 18, 30, 8, 0, 28, 52, 0, 0, 16, 24, 0, 18, 30, 0
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OFFSET
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1,8
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REFERENCES
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See A051664.
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..65537 (terms 1..1000 from T. D. Noe)
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FORMULA
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From Benoit Cloitre, Aug 06 2003: (Start)
a(4n+2) = a(2n+1); a(4n) = a(2n) + phi(2n).
When p is an odd prime and m integer >= 1: a(p^m) = a(2*p^m) = p^m - p^(m-1) - p + 1. In particular a(p) = a(2p) = 0. (End)
a(n) = 1 + phi(n) - A051664(n) - T. D. Noe, Aug 08 2003
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MATHEMATICA
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Table[Count[CoefficientList[Cyclotomic[n, x], x], _?(#==0&)], {n, 0, 100}]
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PROG
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(PARI) a(n)=sum(k=0, eulerphi(n), if(polcoeff(polcyclo(n), k), 0, 1))
(PARI) A086798(n) = (1 + eulerphi(n) - length(select(x->x!=0, Vec(polcyclo(n))))); \\ Antti Karttunen, Sep 21 2018
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CROSSREFS
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Cf. A086765, A086780.
Cf. A051664 (number of nonzero terms in n-th cyclotomic polynomial).
Sequence in context: A025096 A261137 A319341 * A155061 A322016 A247446
Adjacent sequences: A086795 A086796 A086797 * A086799 A086800 A086801
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KEYWORD
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nonn
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 05 2003
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EXTENSIONS
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More terms from Benoit Cloitre and T. D. Noe, Aug 06 2003
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STATUS
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approved
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