A225090 Minimal sum of entries of the character table of a group of order n.

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

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 A345965

Adjacent sequences: A225087 A225088 A225089 * A225091 A225092 A225093

Keyword

nonn

Author

Eric M. Schmidt, Apr 27 2013

Status

approved