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

Author

Reiner Martin, Dec 29 2001

Keywords

• nonn
• nice
• mult
• easy

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.

Crossrefs

Cf. A000001, A056867, A069739.

Programs

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 *)