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URL: https://oeis.org/A297420

⇱ A297420 - OEIS

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A297420
Square of the number of groups of order n.
1
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
0,5
COMMENTS
The record values are 1, 4, 25, 196, 225, 2601, 2704, 71289, 5419584, 3146312464, 110128506489369, 2448999521196387209521, etc. (A046058)
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..2047 [a(1024) corrected by Andrey Zabolotskiy]
FORMULA
a(n) = A000001(n)^2.
MAPLE
with(GroupTheory): 0, seq(NumGroups(n)^2, n=1..100); # Muniru A Asiru, Jan 29 2018
MATHEMATICA
Join[{0}, FiniteGroupCount[Range[200]]^2]
PROG
(Magma) D:=SmallGroupDatabase(); [0] cat [ NumberOfSmallGroups(D, n)^2 : n in [1..100] ];
(GAP) Concatenation([0], List([1..100], n -> NumberSmallGroups(n)^2)); # Muniru A Asiru, Jan 29 2018
CROSSREFS
KEYWORD
nonn,less
AUTHOR
Vincenzo Librandi, Dec 31 2017
EXTENSIONS
Name clarified by Jon E. Schoenfield, May 24 2019
STATUS
approved