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A086823
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Coefficient of x^2 in the n-th cyclotomic polynomial. (The same as the coefficient of x^(phi(n)-2) ).
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1
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0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, -1, 1, 1, 0, 0, 1, 0, 1, -1, 0, 1, 1, 0, 0, 1, 0, -1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, -1, 0, 1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, -1, 0, 0, 1, 0, 1, 1, 0, -1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1
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OFFSET
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1
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..65539
Eric Weisstein's World of Mathematics, Cyclotomic Polynomial
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FORMULA
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If n is odd, a(n) = 1/2 * mu(n)*(mu(n)-1), if n is even, a(n) = 1/2 * mu(n)*(mu(n)-1) - mu(n/2), where mu is Möbius mu function, A008683.
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MATHEMATICA
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mm[n_]:=Module[{c=MoebiusMu[n]}, If[OddQ[n], (c(c-1))/2, (c(c-1))/2-MoebiusMu[ n/2]]]; Array[mm, 110] (* Harvey P. Dale, May 20 2018 *)
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PROG
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(PARI) a(n) = polcoeff(polcyclo(n), 2); \\ David Wasserman
(PARI) A086823(n) = (((1/2)*moebius(n)*(moebius(n)-1)) - if(!(n%2), moebius(n/2))); \\ Antti Karttunen, Sep 27 2018
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CROSSREFS
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Cf. A008683, A000010.
Sequence in context: A131735 A131736 A152228 * A228487 A295306 A295303
Adjacent sequences: A086820 A086821 A086822 * A086824 A086825 A086826
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KEYWORD
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sign
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 07 2003
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EXTENSIONS
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More terms from David Wasserman, Mar 29 2005
Offset corrected by Antti Karttunen, Sep 27 2018
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STATUS
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approved
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