A239699 Numbers n such that the number of Abelian groups of order n is equal to the number of non-Abelian groups of order n.

6, 10, 14, 21, 22, 26, 28, 34, 38, 39, 44, 46, 55, 57, 58, 62, 63, 74, 76, 82, 86, 92, 93, 94, 105, 106, 111, 117, 118, 122, 124, 129, 134, 142, 146, 155, 158, 165, 166, 172, 178, 183, 188, 194, 195, 201, 202, 203, 205, 206, 214, 218, 219, 226, 231, 236, 237

Offset

1,1

Comments

Numbers n such that A000688(n) = A060689(n).

Links

Michel Lagneau, Table of n, a(n) for n = 1..390

Example

6 is in the sequence because there are 2 groups of order 6: 1 commutative group and 1 non-commutative group. Then A000688(6) = A060689(6) = 1.
44 is in the sequence because there are 4 groups of order 44: 2 commutative groups and 2 non-commutative groups. Then A000688(44) = A060689(44) = 2.

Mathematica

lst:={}; f[n_]:=Times@@PartitionsP/@Last/@FactorInteger@n; g[n_]:=FiniteGroupCount[n]-FiniteAbelianGroupCount[n]; Do[If[f[n]==g[n], AppendTo[lst, n]], {n, 500}]; lst

Crossrefs

Cf. A000688, A060689, A238877.

Sequence in context: A315221 A315222 A315223 * A068919 A060650 A350586

Adjacent sequences: A239696 A239697 A239698 * A239700 A239701 A239702

Keyword

nonn

Author

Michel Lagneau, Mar 24 2014

Status

approved