A059806 Minimal size of the center of G where G is a finite group of order n.

1, 2, 3, 4, 5, 1, 7, 2, 9, 1, 11, 1, 13, 1, 15, 2, 17, 1, 19, 1, 1, 1, 23, 1, 25, 1, 3, 2, 29, 1, 31, 2, 33, 1, 35, 1, 37, 1, 1, 2, 41, 1, 43, 2, 45, 1, 47, 1, 49, 1, 51, 1, 53, 1, 1, 1, 1, 1, 59, 1, 61, 1, 3, 2, 65, 1, 67, 1, 69, 1, 71, 1, 73, 1, 1, 2, 77, 1

Offset

1,2

Comments

a(n) = n if and only if n belongs to sequence A051532 - Avi Peretz (njk(AT)netvision.net.il), Feb 27 2001

a(n) = 1 if and only if n occurs in A060702. - Eric M. Schmidt, Aug 27 2012

Links

Eric M. Schmidt, Table of n, a(n) for n = 1..2000

MathOverflow, Center of p-groups

Formula

For prime p and m >= 3, a(p^m) = p. - Eric M. Schmidt, Aug 27 2012

Example

a(6) = 1 because the symmetric group S_3 has trivial center.

Prog

(GAP) A059806 := function(n) local min, fact, i; if (n mod 6 = 0) then return 1; fi; if (IsPrimePowerInt(n)) then fact := Factors(n); if (Length(fact) <> 2) then return fact[1]; fi; fi; min := n; for i in [1..NumberSmallGroups(n)] do min := Minimum(min, Size(Center(SmallGroup(n, i)))); if (min = 1) then break; fi; od; return min; end; # Eric M. Schmidt, Aug 27 2012

Crossrefs

Cf. A059807, A051532.

Sequence in context: A273825 A082299 A081806 * A332425 A286594 A241479

Adjacent sequences: A059803 A059804 A059805 * A059807 A059808 A059809

Keyword

nonn

Author

Noam Katz (noamkj(AT)hotmail.com), Feb 24 2001

Extensions

More terms from Eric M. Schmidt, Aug 27 2012

Status

approved