|
%I #35 Oct 30 2022 18:19:59
%S 1,1,1,2,1,1,1,5,2,1,1,2,1,1,1,14,1,2,1,2,1,1,1,5,2,1,5,2,1,1,1,51,1,
%T 1,1,4,1,1,1,5,1,1,1,2,2,1,1,14,2,2,1,2,1,5,1,5,1,1,1,2,1,1,2,267,1,1,
%U 1,2,1,1,1,10,1,1,2,2,1,1,1,14,15,1,1,2,1,1,1,5,1,2,1,2,1,1,1,51,1,2,2,4,1
%N Number of nilpotent groups of order n.
%C Multiplicative with a(p^m) equal to the number of groups of order p^m.
%H T. D. Noe and Amiram Eldar, <a href="/A066060/b066060.txt">Table of n, a(n) for n = 1..2047</a> (terms 1..2015 from T. D. Noe)
%H John Renze, <a href="http://mathworld.wolfram.com/NilpotentGroup.html">Nilpotent Group</a>.
%t terms = 101; fgc = FiniteGroupCount[Range[terms]]; a[1] = 1; a[n_ /; PrimePowerQ[n] && 1 < n <= terms] := a[n] = fgc[[n]]; a[n_ /; 1 < n <= terms] := a[n] = Times @@ (a[#[[1]]^#[[2]]]& /@ FactorInteger[n]); Array[a, terms] (* _Jean-François Alcover_, Oct 03 2017 *)
%Y Cf. A000001, A056867, A069739.
%K nonn,nice,mult,easy
%O 1,4
%A _Reiner Martin_, Dec 29 2001
|
