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

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, 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, 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

Offset

1,10

References

See A051664

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Formula

a(n) = 0 iff n is a prime power. - T. D. Noe, Aug 08 2003

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

Mathematica

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

Prog

(PARI) a(n) = #select(x->(x<0), Vec(polcyclo(n))); \\ Michel Marcus, Apr 18 2018

Crossrefs

Cf. A086765, A000961.

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

Sequence in context: A193056 A244417 A324811 * A158612 A073430 A371093

Adjacent sequences: A086777 A086778 A086779 * A086781 A086782 A086783

Keyword

nonn

Author

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

Extensions

More terms from T. D. Noe, Aug 08 2003

Status

approved