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 A086823 Coefficient of x^2 in the n-th cyclotomic polynomial. (The same as the coefficient of x^(phi(n)-2) ). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65539 Eric Weisstein's World of Mathematics, Cyclotomic Polynomial FORMULA 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. MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A008683, A000010. Sequence in context: A131735 A131736 A152228 * A228487 A295306 A295303 Adjacent sequences: A086820 A086821 A086822 * A086824 A086825 A086826 KEYWORD sign AUTHOR Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 07 2003 EXTENSIONS More terms from David Wasserman, Mar 29 2005 Offset corrected by Antti Karttunen, Sep 27 2018 STATUS approved

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Last modified March 28 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)