%I A088144
%S A088144 1,2,5,8,23,26,68,57,139,174,123,222,328,257,612,636,886,488,669,
%T A088144 1064,876,1105,1744,1780,1552,2020,1853,2890,1962,2712,2413,3536,
%U A088144 4384,3335,5364,3322,3768,4564,7683,7266,8235,4344,8021,6176,8274
%N A088144 Sum of primitive roots of n-th prime.
%C A088144 From Pieter Moree (moree(AT)science.uva.nl), Nov 03 2003: It is a result 
               that goes back to Mirsky that the set of primes p for which p-1 is 
               squarefree has density A, where A denotes the Artin constant (A = 
               prod_q (1-1/(q(q-1)), q running over all primes). Numerically A = 
               0.3739558136.... More precisely, Sum_{p <= x} mu(p-1)^2 = Ax/log 
               x + o(x/log x) as x tends to infinity. Conjecture: sum_{p <= x, mu(p-1)=1} 
               1 = (A/2)x/log x + o(x\log x) and sum_{p <= x, mu(p-1)=-1} 1 = (A/
               2)x/log x + o(x/log x).
%D A088144 C. F. Gauss, Disquisitiones Arithmeticae.
%D A088144 Leon Mirsky, Amer. Math. Monthly 56 (1949), 17-19.
%H A088144 T. D. Noe, <a href="b088144.txt">Table of n, a(n) for n=1..1000</a>
%e A088144 For 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, the primitive roots are as follows: 
               {{1}, {2}, {2, 3}, {3, 5}, {2, 6, 7, 8}, {2, 6, 7, 11}, {3, 5, 6, 
               7, 10, 11, 12, 14}, {2, 3, 10, 13, 14, 15}, {5, 7, 10, 11, 14, 15, 
               17, 19, 20, 21}, {2, 3, 8, 10, 11, 14, 15, 18, 19, 21, 26, 27}}
%t A088144 PrimitiveRootQ[ a_Integer, p_Integer ] := Block[ {fac, res}, fac = FactorInteger[ 
               p - 1 ]; res = Table[ PowerMod[ a, (p - 1)/fac[ [ i, 1 ] ], p ], 
               {i, Length[ fac ]} ]; ! MemberQ[ res, 1 ] ] PrimitiveRoots[ p_Integer 
               ] := Select[ Range[ p - 1 ], PrimitiveRootQ[ #, p ] & ]
%Y A088144 Sequence in context: A009735 A137095 A092097 this_sequence A100501 A142869 
               A086825
%Y A088144 Adjacent sequences: A088141 A088142 A088143 this_sequence A088145 A088146 
               A088147
%K A088144 nonn
%O A088144 1,2
%A A088144 Ed Pegg Jr (edp(AT)wolfram.com), Nov 03 2003