A340519 Smallest order of a non-abelian group with a center of order n.

6, 8, 18, 16, 30, 24, 42, 32, 54, 40, 66, 48, 78, 56, 90, 64, 102, 72, 114, 80, 126, 88, 138, 96, 150, 104, 162, 112, 174, 120, 186, 128, 198, 136, 210, 144, 222, 152, 234, 160, 246, 168, 258, 176, 270, 184, 282, 192, 294, 200, 306, 208, 318, 216, 330, 224, 342, 232, 354, 240, 366, 248

Offset

1,1

Comments

a(n) is 6n if n is odd and 4n if n is even. This is because the groups involved are C(n) X S3 if n is odd, where S3 is the symmetric group of order 6, and C(n/2) X D8 if n is even, where D8 is the dihedral group of order 8 and C(m) is the cyclic group of order m.

By Lagrange's Theorem a(n) is a multiple of n.

Links

Table of n, a(n) for n=1..62.

Mathematica

Table[If[OddQ[n], 6n, 4n], {n, 100}] (* Harvey P. Dale, Mar 03 2023 *)

Crossrefs

Equals 2*A106833.

Cf. A059806, A060702, A340518.

Sequence in context: A270046 A093479 A239396 * A315942 A315943 A315944

Adjacent sequences: A340516 A340517 A340518 * A340520 A340521 A340522

Keyword

nonn

Author

Bob Heffernan and Des MacHale, Jan 24 2021; corrected Feb 14 2021

Status

approved