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%I #28 Sep 13 2018 10:59:57
%S 1,2,4,8,22,48,156,320,1008,2640,7700,13824,61320,170352,401280,
%T 983040,3796100,7838208,30566592,62304000,229686912,670824000,
%U 2003046356,3583180800,15403487000,48881851200,128672022528,314657860608,1163185915872,2340264960000,9947788640064
%N Number of primitive polynomials of degree n over GF(3).
%C Second row of the array T(n,k) = phi(p^k-1)/k, p=prime(n), which starts
%C 1, 1, 2, 2, 6, 6, 18, 16, ... A011260
%C 1, 2, 4, 8, 22, 48, 156, 320, ... here
%C 2, 4, 20, 48, 280, 720, 5580, 14976, ... A027741
%C 2, 8, 36, 160, 1120, 6048, 37856, 192000, ... A027743
%C 4, 16, 144, 960, 12880, 62208, 1087632, 7027200, ... A319166
%C 4, 24, 240, 1536, 24752, 224640, 2988024, 21934080, ...
%C 8, 48, 816, 5376, 141984, 1057536, 29309904, 224501760, ...
%C - _R. J. Mathar_, Aug 24 2011
%C From _Joerg Arndt_, Oct 03 2012: (Start)
%C Number of base-3, length-n Lyndon words w such that gcd(w, 3^n-1)==1 (where w is interpreted as a radix-3 number); replacing 3 by any prime p gives the analogous statement for GF(p).
%C The statement above is the consequence of the following.
%C Let p be a prime and g be a generator of GF(p^n). If w is a base-p, length-n Lyndon word then f=g^w (where w is interpreted as a radix-p number) has an irreducible characteristic polynomial C (over GF(p)) and, if gcd(w,p^n-1)==1 then C is primitive.
%C (End)
%H Vaclav Kotesovec, <a href="/A027385/b027385.txt">Table of n, a(n) for n = 1..200</a> (terms 1..100 from Seiichi Manyama)
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/TotientFunction.html">MathWorld: Totient Function</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Euler%27s_phi_function">Euler's totient function</a>
%p A027385 := proc(n) numtheory[phi](3^n-1)/n; end proc:
%t Table[EulerPhi[3^n - 1]/n, {n, 1, 30}] (* _Vaclav Kotesovec_, Nov 23 2017 *)
%o (PARI) a(n) = eulerphi(3^n-1)/n; /* _Joerg Arndt_, Aug 25 2011 */
%K nonn
%O 1,2
%A _Frank Ruskey_
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