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

0,3

Links

Table of n, a(n) for n=0..60.

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A151367 A368957 A057648 * A327930 A068511 A306544

Adjacent sequences: A282457 A282458 A282459 * A282461 A282462 A282463

Keyword

nonn

Author

Vincenzo Librandi, Feb 16 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

Status

approved