A225090 - OEIS

%I #15 May 02 2014 03:14:25

%S 1,2,3,4,5,5,7,8,9,8,11,8,13,11,15,14,17,14,19,11,13,17,23,13,25,20,

%T 27,22,29,23,31,26,33,26,35,18,37,29,23,22,41,17,43,34,45,35,47,24,49,

%U 38,51,25,53,30,23,20,33,44,59,19,61,47,39,44,65,50,67,32

%N Minimal sum of entries of the character table of a group of order n.

%C The maximal sum of entries is just n, and this is achieved by any Abelian group of order n.

%C A060653(n) <= a(n) <= n.

%H Eric M. Schmidt, <a href="/A225090/b225090.txt">Table of n, a(n) for n = 1..1023</a>

%H Louis Solomon, <a href="http://dx.doi.org/10.1090/S0002-9939-1961-0132783-8">On the Sum of the Elements in the Character Table of a Finite Group</a>. Proceedings of the American Mathematical Society, Vol. 12, No. 6 (Dec., 1961), pp. 962-963.

%e a(6)=5 because the sum of the entries in the character table of the symmetric group S3 is 5, the minimum for groups of order 6.

%o (GAP) A225090 := function(n) local min, i; min := n; for i in [1..NumberSmallGroups(n)] do min := Minimum(min, Sum(Sum(Irr(SmallGroup(n, i))))); od; return min; end;

%Y Cf. A061064, A082733, A085624, A086808.

%K nonn

%O 1,2

%A _Eric M. Schmidt_, Apr 27 2013