A230798 The number of distinct coefficients in the n-th cyclotomic polynomial.

2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 3, 2, 1, 3, 1, 3, 3, 2, 1, 3, 2, 2, 2, 3, 1, 3, 1, 2, 3, 2, 3, 3, 1, 2, 3, 3, 1, 3, 1, 3, 3, 2, 1, 3, 2, 3, 3, 3, 1, 3, 3, 3, 3, 2, 1, 3, 1, 2, 3, 2, 3, 3, 1, 3, 3, 3, 1, 3, 1, 2, 3, 3, 3, 3, 1, 3, 2, 2, 1, 3, 3, 2

Offset

1,1

Comments

a(n) = 1 if n is a prime.

The sum of the coefficients in the n-th cyclotomic polynomial is given by A020500.

The first occurrence of 4 in this sequence is a(105).

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Example

a(12)=3 because the distinct coefficients of the 12th cyclotomic polynomial, x^4-x^2+1, are 0, 1 and -1.

Mathematica

Table[Length[Union[CoefficientList[Cyclotomic[n, x], x]]], {n, 100}] (* T. D. Noe, Dec 09 2013 *)

Prog

(PARI) a(n) = #vecsort(Vec(polcyclo(n)), , 8)

Crossrefs

Cf. A020500, A230799.

Cf. A231611 (least k for which cyclotomic(k) has n distinct terms).

Sequence in context: A053574 A321944 A065203 * A266224 A029396 A084746

Adjacent sequences: A230795 A230796 A230797 * A230799 A230800 A230801

Keyword

nonn

Author

Colin Barker, Oct 30 2013

Status

approved