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A061064 Maximal number of zeros in the character table of a group with n elements. 2
0, 0, 0, 0, 0, 1, 0, 3, 0, 2, 0, 4, 0, 3, 0, 12, 0, 9, 0, 8, 4, 5, 0, 27, 0, 6, 16, 12, 0, 25, 0, 48, 0, 8, 0, 36, 0, 9, 8, 75, 0, 49, 0, 20, 0, 11, 0, 108, 0, 50, 0, 24, 0, 81, 8, 147, 12, 14, 0, 100, 0, 15, 36, 192, 0, 121, 0, 32, 0, 98, 0, 243, 0, 18, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

A finite non-Abelian group G has an irreducible representation of degree >= 2 and the character of such representation always has a zero; so a(n) = 0 iff every group of order n is Abelian, i.e. n belongs to A051532.

LINKS

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

EXAMPLE

a(6) = 1 because the character table of the symmetric group S_3 is / 1, 1, 1 / 1, 1,-1 / 2,-1, 0 /.

PROG

(GAP) A061064 := function(n) local max, i; max := 0; for i in [1..NumberSmallGroups(n)] do max := Maximum(max, Sum(Irr(SmallGroup(n, i)), chi->Number(chi, x->x=0))); od; return max; end; # Eric M. Schmidt, Aug 24 2012

CROSSREFS

Cf. A051532.

Sequence in context: A019746 A112574 A318652 * A016597 A128114 A065152

Adjacent sequences:  A061061 A061062 A061063 * A061065 A061066 A061067

KEYWORD

nonn,nice

AUTHOR

Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 05 2001

EXTENSIONS

Added terms a(n) for n>=24, Eric M. Schmidt, Aug 24 2012.

STATUS

approved

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Last modified August 19 18:51 EDT 2019. Contains 326133 sequences. (Running on oeis4.)