A086765 Number of positive coefficients in n-th cyclotomic polynomial.

1, 2, 3, 2, 5, 2, 7, 2, 3, 3, 11, 2, 13, 4, 4, 2, 17, 2, 19, 3, 5, 6, 23, 2, 5, 7, 3, 4, 29, 4, 31, 2, 8, 9, 9, 2, 37, 10, 9, 3, 41, 5, 43, 6, 4, 12, 47, 2, 7, 3, 12, 7, 53, 2, 9, 4, 13, 15, 59, 4, 61, 16, 5, 2, 16, 8, 67, 9, 16, 9, 71, 2, 73, 19, 4, 10, 16, 9, 79, 3, 3, 21, 83, 5, 21, 22, 20, 6

Offset

1,2

References

See A051664

Links

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

Formula

If n = p^m is a prime power then a(n) = p.

Example

The 1st cyclotomic polynomial is -1+1*x, which has 1 positive coefficient.
The 2nd cyclotomic polynomial is 1+1*x, which has 2 positive coefficients.
The 4th cyclotomic polynomial s 1+1*x^2, which has 2 positive coefficients.

Mathematica

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

Crossrefs

Cf. A007947.

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

Sequence in context: A080210 A126594 A363895 * A079868 A280697 A088444

Adjacent sequences: A086762 A086763 A086764 * A086766 A086767 A086768

Keyword

nonn

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 02 2003

Extensions

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

Status

approved