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
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