A282460 Number of groups of order n^2.

0, 1, 2, 2, 14, 2, 14, 2, 267, 15, 16, 2, 197, 2, 12, 6, 56092, 2, 176, 2, 221, 13, 12, 2, 8681, 15, 16, 504, 172, 2, 150, 2, 49487367289, 6, 16, 4, 3609, 2, 12, 13, 10281, 2, 228, 2, 167, 63, 12, 2, 15756130, 15, 227, 7, 219, 2, 7199, 15, 8085, 21, 16, 2, 4484

Offset: 0

Author

Vincenzo Librandi, Feb 16 2017

Keywords

• nonn

Links

• David Burrell, On the number of groups of order 1024, Communications in Algebra, 2021, 1-3.
• Max Horn, Numbers of isomorphism types of finite groups of given order

Crossrefs

Cf. A000001, A000679, A140987, A141323, A235388.

Programs

Magma

D:=SmallGroupDatabase(); [0] cat [ NumberOfSmallGroups(D, n^2) : n in [1..31] ];

Mathematica

Join[{0}, FiniteGroupCount[Range[45]^2]]

Formula

a(n) = A000001(n^2). - R. J. Mathar, Feb 23 2017

Extensions

a(32) corrected by David Burrell, Jun 07 2022

Terms a(46) and beyond from Max Horn's website added by Andrey Zabolotskiy, May 14 2023