A230799 The number of distinct nonzero coefficients in the n-th cyclotomic polynomial.

2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2

Offset

1,1

Comments

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(330).

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Example

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

Maple

A230799 := n -> nops({coeffs(numtheory[cyclotomic](n, z), z)}):
seq(A230799(n), n=1..86);  # Peter Luschny, Oct 30 2013

Mathematica

a[n_] := List @@ Cyclotomic[n, x] /. x -> 1 // Union // Length;
Array[a, 100] (* Jean-François Alcover, Jul 08 2019 *)

Prog

(PARI) a(n) = v=vecsort(Vec(polcyclo(n)), , 8); if(has_zero(v), #v-1, #v)
has_zero(v) = for(i=1, #v, if(v[i]==0, return(1))); 0
(PARI) {a(n) = if( n<1, 0, #setminus( Set( Vec( polcyclo(n))), [0]))};
/* Michael Somos, Mar 27 2014 */

Crossrefs

Cf. A020500, A230798.

Sequence in context: A321650 A205007 A078470 * A279496 A151683 A133912

Adjacent sequences: A230796 A230797 A230798 * A230800 A230801 A230802

Keyword

nonn

Author

Colin Barker, Oct 30 2013

Status

approved