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A086765 Number of positive coefficients in n-th cyclotomic polynomial. 5

%I #9 Sep 15 2012 14:14:24

%S 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,

%T 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,

%U 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

%N Number of positive coefficients in n-th cyclotomic polynomial.

%D See A051664

%H T. D. Noe, <a href="/A086765/b086765.txt">Table of n, a(n) for n=1..1000</a>

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

%e The 1st cyclotomic polynomial is -1+1*x, which has 1 positive coefficient.

%e The 2nd cyclotomic polynomial is 1+1*x, which has 2 positive coefficients.

%e The 4th cyclotomic polynomial s 1+1*x^2, which has 2 positive coefficients.

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

%Y Cf. A007947.

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

%K nonn

%O 1,2

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

%E More terms from _T. D. Noe_, Aug 08 2003

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