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

%I A086765 #9 Sep 15 2012 14:14:24
%S A086765 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 A086765 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 A086765 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 A086765 Number of positive coefficients in n-th cyclotomic polynomial.
%D A086765 See A051664
%H A086765 T. D. Noe, <a href="/A086765/b086765.txt">Table of n, a(n) for n=1..1000</a>
%F A086765 If n = p^m is a prime power then a(n) = p.
%e A086765 The 1st cyclotomic polynomial is -1+1*x, which has 1 positive coefficient.
%e A086765 The 2nd cyclotomic polynomial is 1+1*x, which has 2 positive coefficients.
%e A086765 The 4th cyclotomic polynomial s 1+1*x^2, which has 2 positive coefficients.
%t A086765 Table[Count[CoefficientList[Cyclotomic[n, x], x], _?(#>0&)], {n, 0, 100}]
%Y A086765 Cf. A007947.
%Y A086765 Cf. A051664 (number of nonzero terms in n-th cyclotomic polynomial).
%K A086765 nonn
%O A086765 1,2
%A A086765 Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 02 2003
%E A086765 More terms from _T. D. Noe_, Aug 08 2003