A141323 -id:A141323 - cp's OEIS frontend

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

Vincenzo Librandi, Feb 16 2017

nonn

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

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

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

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

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

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

A297420 Square of the number of groups of order n.

Original entry on oeis.org

0, 1, 1, 1, 4, 1, 4, 1, 25, 4, 4, 1, 25, 1, 4, 1, 196, 1, 25, 1, 25, 4, 4, 1, 225, 4, 4, 25, 16, 1, 16, 1, 2601, 1, 4, 1, 196, 1, 4, 4, 196, 1, 36, 1, 16, 4, 4, 1, 2704, 4, 25, 1, 25, 1, 225, 4, 169, 4, 4, 1, 169, 1, 4, 16, 71289, 1, 16, 1, 25, 1, 16, 1, 2500

Offset: 0

Vincenzo Librandi, Dec 31 2017

The record values are 1, 4, 25, 196, 225, 2601, 2704, 71289, 5419584, 3146312464, 110128506489369, 2448999521196387209521, etc. (A046058)

Vincenzo Librandi, Table of n, a(n) for n = 0..2047 [a(1024) corrected by Andrey Zabolotskiy]

Cf. A000001, A000679, A140987, A141323, A235388, A282460.

Concatenation([0], List([1..100], n -> NumberSmallGroups(n)^2)); # Muniru A Asiru, Jan 29 2018

D:=SmallGroupDatabase(); [0] cat [ NumberOfSmallGroups(D, n)^2 : n in [1..100] ];

with(GroupTheory):  0,seq(NumGroups(n)^2, n=1..100); # Muniru A Asiru, Jan 29 2018

Join[{0}, FiniteGroupCount[Range[200]]^2]

a(n) = A000001(n)^2.

Name clarified by Jon E. Schoenfield, May 24 2019

cp's OEIS Frontend

A282460 Number of groups of order n^2.

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