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Search: id:A075795
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| A075795 |
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Number of k, 0<k<=n, such that the resultant of the k-th cyclotomic polynomial and the n-th cyclotomic polynomial is equal to 1. |
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+0
1
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| 0, 0, 1, 1, 3, 3, 5, 4, 6, 7, 9, 8, 11, 11, 12, 11, 15, 14, 17, 16, 18, 19, 21, 19, 22, 23, 23, 24, 27, 2, 6, 29, 26, 30, 31, 32, 31, 35, 35, 36, 35, 39, 38, 41, 40, 41, 43, 45, 42, 46, 46, 48, 48, 51, 49, 52, 51, 54, 55, 57, 55, 59, 59, 59, 57, 62, 62, 65, 64, 66, 66, 69, 66, 71
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OFFSET
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1,5
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COMMENT
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a(n)>=phi(n) since if (k,n)=1, then res(polcyclo(n),polcyclo(k))=1.
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REFERENCES
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Apostol, T. M. "Resultants of Cyclotomic Polynomials." Proc. Amer. Math. Soc. 24, 457-462, 1970.
Apostol, T. M. "The Resultant of the Cyclotomic Polynomials and ..." Math. Comput. 29, 1-6, 1975.
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LINKS
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E. M. Weisstein, Cyclotomic polynomials
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FORMULA
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a(n) = n-A073093(n)
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PROGRAM
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(PARI) a(n)=sum(k=1, n, if(1-polresultant(polcyclo(n), polcyclo(k)), 0, 1))
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CROSSREFS
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Cf. A054372, A073093.
Sequence in context: A131950 A116192 A090104 this_sequence A058268 A087851 A087852
Adjacent sequences: A075792 A075793 A075794 this_sequence A075796 A075797 A075798
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 13 2002
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