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A225090
Minimal sum of entries of the character table of a group of order n.
1
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, 27, 22, 29, 23, 31, 26, 33, 26, 35, 18, 37, 29, 23, 22, 41, 17, 43, 34, 45, 35, 47, 24, 49, 38, 51, 25, 53, 30, 23, 20, 33, 44, 59, 19, 61, 47, 39, 44, 65, 50, 67, 32
OFFSET
1,2
COMMENTS
The maximal sum of entries is just n, and this is achieved by any Abelian group of order n.
A060653(n) <= a(n) <= n.
LINKS
Louis Solomon, On the Sum of the Elements in the Character Table of a Finite Group. Proceedings of the American Mathematical Society, Vol. 12, No. 6 (Dec., 1961), pp. 962-963.
EXAMPLE
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.
PROG
(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;
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric M. Schmidt, Apr 27 2013
STATUS
approved