A209938 Number of groups of order prime(n)^5 with nontrivial unramified Brauer groups.

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

Michael B. Porter, Table of n, a(n) for n = 3..10000

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: A245297 A002421 A360828 * A165953 A045885 A019118

Adjacent sequences: A209935 A209936 A209937 * A209939 A209940 A209941

Keyword

nonn,easy

Author

Jonathan Vos Post, Mar 15 2012

Status

approved