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A209938
Number of groups of order prime(n)^5 with nontrivial unramified Brauer groups.
1
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, 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, 6, 4, 6, 8, 6, 4, 6, 8, 6, 8, 4, 8, 4, 8, 6, 4, 6, 8, 6
OFFSET
3,1
COMMENTS
From Michael B. Porter, Mar 17 2012: (Start)
The values of a(n) are always 4, 6, or 8. To be exact:
a(n)=8 if prime(n) is 1 (mod 12),
a(n)=6 if prime(n) is 5 or 7 (mod 12), and
a(n)=4 if prime(n) is 11 (mod 12). (End)
LINKS
Primoz Moravec, Groups of order p^5 and their unramified Brauer groups, arXiv:1203.3289v1 [math.GR], 2012.
FORMULA
For p > 3, a(p) = gcd(p-1,4) + gcd(p-1,3) + 1.
EXAMPLE
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.
PROG
(PARI) A209938(n) = gcd(prime(n)-1, 4)+gcd(prime(n)-1, 3)+1 \\ Michael B. Porter, Mar 17 2012
CROSSREFS
Sequence in context: A371504 A002421 A360828 * A165953 A045885 A019118
KEYWORD
nonn,easy
AUTHOR
Jonathan Vos Post, Mar 15 2012
STATUS
approved