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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 (list; graph; refs; listen; history; text; internal format)
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

Eric M. Schmidt, Table of n, a(n) for n = 1..1023

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

Cf. A061064, A082733, A085624, A086808.

Sequence in context: A269524 A161656 A306328 * A162683 A073137 A131233

Adjacent sequences:  A225087 A225088 A225089 * A225091 A225092 A225093

KEYWORD

nonn

AUTHOR

Eric M. Schmidt, Apr 27 2013

STATUS

approved

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Last modified July 22 10:03 EDT 2019. Contains 325219 sequences. (Running on oeis4.)