A238877 Members of a pair (a,b) such that a is the number of Abelian groups of order n and b is the number of non-Abelian groups of order n.

1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 1, 1, 0, 3, 2, 2, 0, 1, 1, 1, 0, 2, 3, 1, 0, 1, 1, 1, 0, 5, 9, 1, 0, 2, 3, 1, 0, 2, 3, 1, 1, 1, 1, 1, 0, 3, 12, 2, 0, 1, 1, 3, 2, 2, 2, 1, 0, 1, 3, 1, 0, 7, 44, 1, 0, 1, 1, 1, 0, 4, 10, 1, 0, 1, 1, 1, 1, 3, 11, 1, 0, 1, 5, 1, 0

Offset: 1

Author

Michel Lagneau, Mar 24 2014

Keywords

• nonn

Comments

Pairs (A000688(n),A060689(n)).

Examples

			The 8th pair {3,2} is in the sequence because there exists 5 finite groups of order 8: 3 Abelian groups and 2 non-Abelian groups.
		

Links

• Michel Lagneau, Table of n, a(n) for n = 1..4000 [2nd term in the 1024th pair corrected by Andrey Zabolotskiy]

Crossrefs

Cf. A000001, A000688, A060689.

Programs

Mathematica

lst:={};f[n_]:=Times@@PartitionsP/@Last/@FactorInteger@n;g[n_]:=FiniteGroupCount[n]-FiniteAbelianGroupCount[n];Do[AppendTo[lst,{f[n],g[n]}],{n,80}];Flatten[lst]