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

1,7

Comments

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

Links

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

Example

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.

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]

Crossrefs

Cf. A000001, A000688, A060689.

Sequence in context: A360616 A050370 A050374 * A047886 A239366 A014944

Adjacent sequences: A238874 A238875 A238876 * A238878 A238879 A238880

Keyword

nonn

Author

Michel Lagneau, Mar 24 2014

Status

approved