A297420 Square of the number of groups of order n.
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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..2047 [a(1024) corrected by Andrey Zabolotskiy]
Programs
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GAP
Concatenation([0], List([1..100], n -> NumberSmallGroups(n)^2)); # Muniru A Asiru, Jan 29 2018
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Magma
D:=SmallGroupDatabase(); [0] cat [ NumberOfSmallGroups(D, n)^2 : n in [1..100] ];
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Maple
with(GroupTheory): 0,seq(NumGroups(n)^2, n=1..100); # Muniru A Asiru, Jan 29 2018
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Mathematica
Join[{0}, FiniteGroupCount[Range[200]]^2]
Formula
a(n) = A000001(n)^2.
Extensions
Name clarified by Jon E. Schoenfield, May 24 2019
Comments