cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A086780 Number of negative terms in n-th cyclotomic polynomial.

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%I A086780 #29 Apr 21 2018 06:44:09
%S A086780 1,0,0,0,0,1,0,0,0,2,0,1,0,3,3,0,0,1,0,2,4,5,0,1,0,6,0,3,0,3,0,0,7,8,
%T A086780 8,1,0,9,8,2,0,4,0,5,3,11,0,1,0,2,11,6,0,1,8,3,12,14,0,3,0,15,4,0,15,
%U A086780 7,0,8,15,8,0,1,0,18,3,9,15,8,0,2,0,20,0,4,20,21,19,5,0,3,11,11,20,23,15,1
%N A086780 Number of negative terms in n-th cyclotomic polynomial.
%D A086780 See A051664
%H A086780 T. D. Noe, <a href="/A086780/b086780.txt">Table of n, a(n) for n = 1..1000</a>
%F A086780 a(n) = 0 iff n is a prime power. - _T. D. Noe_, Aug 08 2003
%F A086780 a(n) = (A051664(n)-1)/2 if n is not a prime power and has at most two distinct odd prime divisors. So 105 is the smallest n>1 where neither formula applies. - _Aaron Meyerowitz_, Apr 18 2018
%t A086780 Table[Count[CoefficientList[Cyclotomic[n, x], x], _?(#<0&)], {n, 0, 100}]
%o A086780 (PARI) a(n) = #select(x->(x<0), Vec(polcyclo(n))); \\ _Michel Marcus_, Apr 18 2018
%Y A086780 Cf. A086765, A000961.
%Y A086780 Cf. A051664 (number of nonzero terms in n-th cyclotomic polynomial).
%K A086780 nonn
%O A086780 1,10
%A A086780 Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 03 2003
%E A086780 More terms from _T. D. Noe_, Aug 08 2003