A066060 Number of nilpotent groups of order n.

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, 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, 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

Offset

1,4

Comments

Multiplicative with a(p^m) equal to the number of groups of order p^m.

Links

T. D. Noe and Amiram Eldar, Table of n, a(n) for n = 1..2047 (terms 1..2015 from T. D. Noe)

John Renze, Nilpotent Group.

Mathematica

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 *)

Crossrefs

Cf. A000001, A056867, A069739.

Sequence in context: A343233 A155586 A069739 * A008550 A064094 A090182

Adjacent sequences: A066057 A066058 A066059 * A066061 A066062 A066063

Keyword

nonn,nice,mult,easy

Author

Reiner Martin, Dec 29 2001

Status

approved