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Search: id:A033949
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| A033949 |
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Positive integers that do not have a primitive root. |
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+0
7
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| 8, 12, 15, 16, 20, 21, 24, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 51, 52, 55, 56, 57, 60, 63, 64, 65, 66, 68, 69, 70, 72, 75, 76, 77, 78, 80, 84, 85, 87, 88, 90, 91, 92, 93, 95, 96, 99, 100, 102, 104, 105, 108, 110, 111, 112, 114, 115, 116, 117, 119, 120, 123
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Numbers n such that the cyclotomic polynomial Phi(n,x) is reducible over Zp for all primes p. Harrison shows that this is equivalent to n>2 and the discriminant of Phi(n,x), A004124(n), being a square. - T. D. Noe (noe(AT)sspectra.com), Nov 06 2007
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REFERENCES
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I. Niven and H. S. Zuckerman, An Introduction to the Theory of Numbers, 4th edition, page 62, Theorem 2.25.
Brett A. Harrison, On the reducibility of cyclotomic polynomials over finite fields, Amer. Math. Monthly, Vol 114, No. 9, 813-818.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
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Positive integers except 1, 2, 4 and numbers of the form p^i and 2p^i, where p is an odd prime and i >= 1.
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CROSSREFS
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Cf. A033948.
Sequence in context: A114414 A032455 A050275 this_sequence A062373 A031034 A152758
Adjacent sequences: A033946 A033947 A033948 this_sequence A033950 A033951 A033952
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KEYWORD
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nonn
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AUTHOR
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Calculated by Jud McCranie (j.mccranie(AT)comcast.net)
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