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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.
2
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Mar 24 2014
STATUS
approved