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A060702 Orders of finite groups that have trivial center. 3
1, 6, 10, 12, 14, 18, 20, 21, 22, 24, 26, 30, 34, 36, 38, 39, 42, 46, 48, 50, 52, 54, 55, 56, 57, 58, 60, 62, 66, 68, 70, 72, 74, 75, 78, 80, 82, 84, 86, 90, 93, 94, 96, 98, 100, 102, 106, 108, 110, 111, 114, 116, 118, 120, 122, 126, 129, 130, 132, 134, 136 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Apart from the first element 1 this is a subsequence of A056868 because a nilpotent group has nontrivial center. If n = 0 mod 6 or n >= 6 and n = 2 mod 4 then n is in this sequence.

If n >= 6 and n == 2 mod 4 then n is a member of the sequence because of the dihedral group of order 2(2k+1). In addition, if p is a prime and p == 1 mod 4 then n=4p is a member of the sequence; however, if p == 3 mod 4 and p>5, then n=4p is not a member of the sequence. Furthermore, if n=pq where p and q are distinct odd primes with p<q, then pq belongs to the sequence if and only if p divides q-1. - Des MacHale and Mossie Crowe, Jul 05 2005

This sequence is closed under multiplication. - Eric M. Schmidt, Aug 27 2012

LINKS

Eric M. Schmidt, Table of n, a(n) for n = 1..1000

EXAMPLE

The symmetric group S_3 of order 6 has trivial center so 6 belongs to the sequence.

CROSSREFS

Cf. A056868, A059806.

Sequence in context: A161543 A056868 A069209 * A054741 A177712 A176552

Adjacent sequences:  A060699 A060700 A060701 * A060703 A060704 A060705

KEYWORD

nonn

AUTHOR

Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 20 2001

EXTENSIONS

The old entry 89 was an error, since it is a prime. - Robert F. Bailey (robertb(AT)math.carleton.ca) and Brett Stevens (brett(AT)math.carleton.ca), Jul 16 2009

Sequence extended and corrected by Eric M. Schmidt, Aug 27 2012

STATUS

approved

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Last modified May 29 05:00 EDT 2022. Contains 354122 sequences. (Running on oeis4.)