A086780 - OEIS

%I #29 Apr 21 2018 06:44:09

%S 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 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 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 Number of negative terms in n-th cyclotomic polynomial.

%D See A051664

%H T. D. Noe, <a href="/A086780/b086780.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = 0 iff n is a prime power. - _T. D. Noe_, Aug 08 2003

%F 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 Table[Count[CoefficientList[Cyclotomic[n, x], x], _?(#<0&)], {n, 0, 100}]

%o (PARI) a(n) = #select(x->(x<0), Vec(polcyclo(n))); \\ _Michel Marcus_, Apr 18 2018

%Y Cf. A086765, A000961.

%Y Cf. A051664 (number of nonzero terms in n-th cyclotomic polynomial).

%K nonn

%O 1,10

%A Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 03 2003

%E More terms from _T. D. Noe_, Aug 08 2003