%I #9 Sep 08 2022 08:45:30
%S 1,1,2,1,1,5,2,1,1,14,1,1,1,2,5,1,1,51,1,1,1,1,2,1,1,1,267,1,1,1,1,15,
%T 1,1,1,1,1,1,1,1,2,5,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U 67,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,5,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N Number of groups of order A128603(n).
%C Number of groups whose order divides p^6 for p a prime.
%C The groups of these orders (up to A128603(54403784) = 1073741789 in version V2.13-4) form a class contained in the Small Groups Library of MAGMA. (corrected Mar 18 2007)
%H Klaus Brockhaus, <a href="/A128604/b128604.txt">Table of n, a(n) for n = 1..10000</a>
%H MAGMA Documentation, <a href="http://magma.maths.usyd.edu.au/magma/htmlhelp/text404.htm">Database of Small Groups</a>
%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F a(n) = A000001(A128603(n)).
%e A128603(10) = 16 and there are 14 groups of order 16 (A000001(16) = 14), hence a(10) = 14.
%o (Magma) D:=SmallGroupDatabase(); [ NumberOfSmallGroups(D, n) : n in [ k: k in [1..455] | exists(t) {x: x in [t: t in [1..6] ] | IsPower(k, x) and IsPrime(Iroot(k, x)) } ] ];
%Y Cf. A000001 (number of groups of order n), A128603 (numbers dividing p^6 for p a prime), A098885 (number of groups of prime power orders).
%K nonn
%O 1,3
%A _Klaus Brockhaus_, Mar 13 2007
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