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%I #23 Feb 11 2020 10:47:53
%S 6,6,4,8,6,6,4,6,6,8,6,6,4,6,4,8,6,4,8,6,4,6,8,6,6,4,8,6,6,4,6,6,6,6,
%T 8,6,4,6,4,8,4,8,6,6,6,6,4,8,6,4,8,4,6,4,6,6,8,6,6,6,6,4,8,6,6,8,4,8,
%U 6,4,6,8,6,4,6,8,6,8,4,8,4,8,6,4,6,8,6
%N Number of groups of order prime(n)^5 with nontrivial unramified Brauer groups.
%C From _Michael B. Porter_, Mar 17 2012: (Start)
%C The values of a(n) are always 4, 6, or 8. To be exact:
%C a(n)=8 if prime(n) is 1 (mod 12),
%C a(n)=6 if prime(n) is 5 or 7 (mod 12), and
%C a(n)=4 if prime(n) is 11 (mod 12). (End)
%H Michael B. Porter, <a href="/A209938/b209938.txt">Table of n, a(n) for n = 3..10000</a>
%H Primoz Moravec, <a href="http://arxiv.org/abs/1203.3289">Groups of order p^5 and their unramified Brauer groups</a>, arXiv:1203.3289v1 [math.GR], 2012.
%F For p > 3, a(p) = gcd(p-1,4) + gcd(p-1,3) + 1.
%e prime(8) = 19, so a(8) = gcd(19-1,4) + gcd(19-1,3) + 1 = gcd(18,4) + gcd(18,3) + 1 = 2 + 3 + 1 = 6.
%o (PARI) A209938(n) = gcd(prime(n)-1,4)+gcd(prime(n)-1,3)+1 \\ _Michael B. Porter_, Mar 17 2012
%K nonn,easy
%O 3,1
%A _Jonathan Vos Post_, Mar 15 2012
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