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
Keywords
Examples
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.
Links
- Michel Lagneau, Table of n, a(n) for n = 1..390
Programs
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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
Comments