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

Author

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

Keywords

• nonn

Examples

			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.
		

References

• See A051664

Links

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

Crossrefs

Cf. A007947.

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

Programs

Mathematica

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

Formula

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

Extensions

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