A060938 Maximal degree of an irreducible representation of a group with n elements.

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 4, 3, 2, 1, 3, 1, 2, 3, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 3, 4, 1, 6, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 6, 5, 7, 3, 2, 1, 5, 1, 2, 3, 4, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 3, 2, 1, 6, 1, 5, 3, 2, 1, 6, 1, 2, 1

Offset: 1

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), May 07 2001

Keywords

• nonn

Comments

a(n) = 1 iff every group of order n is Abelian i.e. n belongs to sequence A051532.

a(m)a(n) <= a(mn). - Eric M. Schmidt, Oct 17 2012

Examples

			a(6) = 2 because for the Abelian group with 6 elements the degrees are all 1 and for the symmetric group S_3 the degrees are 1,1,2.
		

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..1535

Crossrefs

Cf. A051532.

Programs

GAP

A060938 := function(n) local max, divs, maxpos, degs, i; if (n=1) then return 1; fi; divs := DivisorsInt(n); maxpos := divs[Int(Length(divs)/2)]; max := 1; for i in [1..NumberSmallGroups(n)] do degs := CharacterDegrees(SmallGroup(n, i)); max := Maximum(max, degs[Length(degs)][1]); if (max = maxpos) then return max; fi; od; return max; end;

Extensions

More terms from Eric M. Schmidt, Oct 17 2012