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A340519 Smallest order of a non-abelian group with a center of order n. 0
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 (list; graph; refs; listen; history; text; internal format)
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.

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

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Last modified October 3 06:40 EDT 2022. Contains 357231 sequences. (Running on oeis4.)