%I A033949
%S A033949 8,12,15,16,20,21,24,28,30,32,33,35,36,39,40,42,44,45,48,51,52,55,56,
%T A033949 57,60,63,64,65,66,68,69,70,72,75,76,77,78,80,84,85,87,88,90,91,92,93,
%U A033949 95,96,99,100,102,104,105,108,110,111,112,114,115,116,117,119,120,123
%N A033949 Positive integers that do not have a primitive root.
%C A033949 Numbers n such that the cyclotomic polynomial Phi(n,x) is reducible over 
               Zp for all primes p. Harrison shows that this is equivalent to n>
               2 and the discriminant of Phi(n,x), A004124(n), being a square. - 
               T. D. Noe (noe(AT)sspectra.com), Nov 06 2007
%D A033949 I. Niven and H. S. Zuckerman, An Introduction to the Theory of Numbers, 
               4th edition, page 62, Theorem 2.25.
%D A033949 Brett A. Harrison, On the reducibility of cyclotomic polynomials over 
               finite fields, Amer. Math. Monthly, Vol 114, No. 9, 813-818.
%H A033949 T. D. Noe, <a href="b033949.txt">Table of n, a(n) for n=1..10000</a>
%F A033949 Positive integers except 1, 2, 4 and numbers of the form p^i and 2p^i, 
               where p is an odd prime and i >= 1.
%Y A033949 Cf. A033948.
%Y A033949 Sequence in context: A114414 A032455 A050275 this_sequence A062373 A031034 
               A152758
%Y A033949 Adjacent sequences: A033946 A033947 A033948 this_sequence A033950 A033951 
               A033952
%K A033949 nonn
%O A033949 1,1
%A A033949 Calculated by Jud McCranie (j.mccranie(AT)comcast.net)