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Search: id:A095877
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| A095877 |
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Numbers n such that the middle coefficient of the cyclotomic polynomial Phi_n(x) has a value not obtained for any smaller n. |
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+0
3
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| 3, 4, 6, 385, 1155, 4785, 6545, 7735, 10101, 11305, 14105, 17255, 18445, 20615, 22165, 22715, 26565, 28985, 33915, 35581, 36295, 37961, 40755, 47355, 49665, 51765
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OFFSET
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1,1
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COMMENT
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Note that for n > 6, we need examine only squarefree n having three or more factors. Sequence A095878 has the values of the middle coefficient of Phi_n(x) for the n in this sequence. Note that for n = 1 and 2, Phi_n(x) is a polynomial having no middle term.
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REFERENCES
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G. Dresden, On the Middle Coefficient of the Cyclotomic Polynomial, MAA Monthly 111 (2004), 531--533.
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LINKS
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G. Dresden, On the Middle Coefficient of the Cyclotomic Polynomial (MAA Monthly, 2004, 531 - 533).
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EXAMPLE
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385 is in this sequence because the middle coefficient of Phi_385(x) is -3, which does not occur for any n < 385.
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MATHEMATICA
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vals={1, 0, -1}; lst={3, 4, 6}; Do[pwrs=Transpose[FactorInteger[n]][[2]]; If[Length[pwrs]>2 && 1==Times@@pwrs, c=Coefficient[Cyclotomic[n, x], x, EulerPhi[n]/2]; If[ !MemberQ[vals, c], AppendTo[lst, n]; AppendTo[vals, c]]], {n, 7, 50000, 2}]; lst
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CROSSREFS
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Cf. A094754 (middle coefficient of cyclotomic polynomial Phi_n(x)).
Adjacent sequences: A095874 A095875 A095876 this_sequence A095878 A095879 A095880
Sequence in context: A066466 A129293 A049010 this_sequence A024476 A093087 A130893
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KEYWORD
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hard,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jun 10 2004
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