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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 Muniru A Asiru, Table of n, a(n) for n = 1..500 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 Adjacent sequences: A201730 A201731 A201732 * A201734 A201735 A201736 KEYWORD nonn AUTHOR W. Edwin Clark, Dec 04 2011 STATUS approved

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Last modified December 2 15:00 EST 2022. Contains 358510 sequences. (Running on oeis4.)