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Search: id:A086798
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| A086798 |
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Number of coefficients equal to zero in n-th cyclotomic polynomial. |
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+0
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
(list; graph; listen)
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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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T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
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a(4n+2)=a(2n+1); a(4n)=a(2n)+phi(2n); if 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. - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 06 2003
a(n) = 1 + phi(n) - A051664(n) - T. D. Noe (noe(AT)sspectra.com), 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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PROGRAM
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(PARI) a(n)=sum(k=0, eulerphi(n), if(polcoeff(polcyclo(n), k), 0, 1))
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CROSSREFS
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Cf. A086765, A086780.
Cf. A051664 (number of nonzero terms in n-th cyclotomic polynomial).
Adjacent sequences: A086795 A086796 A086797 this_sequence A086799 A086800 A086801
Sequence in context: A045951 A025120 A025096 this_sequence A131099 A098800 A087666
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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 (benoit7848c(AT)orange.fr) and T. D. Noe (noe(AT)sspectra.com), Aug 06 2003
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