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A086765
Number of positive coefficients in n-th cyclotomic polynomial.
5
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
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
KEYWORD
nonn
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 02 2003
EXTENSIONS
More terms from T. D. Noe, Aug 08 2003
STATUS
approved