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A201733 Number of isomorphism classes of polycyclic groups (or solvable groups) of order n. 1
1, 1, 1, 2, 1, 2, 1, 5, 2, 2, 1, 5, 1, 2, 1, 14, 1, 5, 1, 5, 2, 2, 1, 15, 2, 2, 5, 4, 1, 4, 1, 51, 1, 2, 1, 14, 1, 2, 2, 14, 1, 6, 1, 4, 2, 2, 1, 52, 2, 5, 1, 5, 1, 15, 2, 13, 2, 2, 1, 12, 1, 2, 4, 267, 1, 4, 1, 5, 1, 4, 1, 50, 1, 2, 3, 4, 1, 6, 1, 52, 15, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
For finite groups solvable is equivalent to polycyclic.
LINKS
Wikipedia, Polycyclic group
Wikipedia, Solvable group
FORMULA
a(n) = A000001(n) for n < 60.
a(n) <= A000001(n) with equality if and only if n is not in A056866. In particular a(n) = A000001(n) for odd n (this is the Feit-Thompson theorem). - Benoit Jubin, Mar 30 2012
PROG
(GAP)
a:=[];;
N:=120;;
for n in [1..N] do
a[n]:=0;;
for j in [1..NrSmallGroups(n)] do
if IsPcGroup(SmallGroup(n, j)) = true then
a[n]:=a[n]+1;
fi;
od;
Print(a[n], ", ");
od;
CROSSREFS
Sequence in context: A318475 A066083 A128644 * A000001 A172133 A146002
KEYWORD
nonn
AUTHOR
W. Edwin Clark, Dec 04 2011
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)